One of the most common questions I get from viewers of the channel is about learning shell Scripting especially those that are new to Linux just switching to Linux and they really want to dive a little deeper into Linux They want to learn some basics They want to learn the basics of the bash shell and bash scripting And I think one of the best tools to play around with to learn bash scripting is actually D-menu for those that are not familiar with what D-menu is. It's basically most people think of it as a run launcher It's more than a run launcher if I hit this key binding here I get a run launcher here at the top of my screen and I can start typing for a program that's installed on my system like Alacrity I could hit enter and it launches the Alacrity terminal But D-menu is more than just a run launcher D-menu actually You can pipe any information you want to into D-menu and D-menu will display it as a menu and because the Possibilities are endless of what you can do with it, especially once you get into scripting with D-menu I think it's a really nifty little tool for you guys to start using to practice your shell scripting So in preparation for making this video I knew I was gonna make this video of several days ago and what I wanted to do is I went into some of my Personal D-menu scripts and I started cleaning them up a little bit getting them ready for you know Displaying to the public and what I did is I actually created a repository over on my git lab if you go to git lab Slash DWT one slash DM scripts for D-menu scripts. Not very original. This is a repository I created I've got I don't know seven or eight of my D-menu scripts listed in that repository for you guys to check out I'm not a programmer by trade So there may be errors in the code some of the scripts are very quick and dirty scripts that I just threw together Just mainly as proof of concepts. So let me show you some of these scripts I'll show you a little bit of the code how the code works and I'll show you of course the scripts in action So let me switch back over to my desktop and I open doom emacs here This is my text editor of choice these days doom emacs I'm going to toggle on big font mode. So you guys can see really big font and I'm going to navigate to this directory here DM scripts and I'll just open it up in dear Ed Which is the built-in file manager here in emacs and I can navigate down and I have several scripts here I think the one that is the simplest as far as the concept is this one here that I call DM comp and it's very It may look complicated, but it's actually dead simple This thing literally I could have wrote it in like two minutes had it not involved so much typing It really involves this Declaring and options array So declare dash a we're going to declare an array and we're going to name it options Equals and then each line is an option in this array And then we're going to pipe all of these options into D menu Now let me show you this in action. So we hit the key combination for this here And you see I have this run prompt that says edit config and it lists Everything that was in that array. So let me escape out of that and I show you once again This is the array now dollar sign home in all caps, of course expands to my actual path to my home directory Which is slash home slash DT. So they do that again You see dollar sign home is replaced by home slash DT in all of these now again I didn't put a lot of thought and effort into this script It's a very quick and dirty script that I just threw together kind of fast But my thinking behind it was I wanted to create this array and in this array all of these options I wanted each option to have three fields I wanted the name of the program that I wanted to edit that particular config file for And then the second field is going to be a dash And then the third field is going to be the path to the config file that I want to be able to edit I know that that may seem a little strange, but what I'm going to do is later I'm going to through the magic of the awk command awk is a command line program that allows you to pull certain fields out of text You know, I'm going to pull the first column out of this later And I'm going to pull the third column out of this later, which is the path to the individual config files themselves So let's get past the array because really like 80% of the script is the comments at the top Me setting a variable for the text editor I want to use because of course these config files need to open in a text editor and I'm going to want them to open in Emacs So that's why I set this variable later. We'll use that variable in a bit And then most of this is declaring the options array here And then listing all of the config files that I commonly edit So I created that list and then down here I have a piping the above array into D menu So I created choice. So this variable is going to be called choice And it's going to run the command printf we're going to print everything in the options array That's what the at sign it means. It means we want all members of the options array printed out And I want you to pipe that into D menu dash I for searching for case insensitively Dash L for I want it to be a vertical list and I want the number of lines to be 20 Dash P is the prompt flag for D menu meaning what prompt do you want And then in single quotes, this is the name of the prompt edit config So again, I do the key binding to launch that you see edit config as the prompt you see the array Now that's not very useful until you also finish the script and tell it what to do when you select an option. So what happens when I select, for example, the very first thing in the array, which is alacrity, it's already highlighted my alacrity config. Well, what I want you to do is if choice remember choice was the variable we created for everything being piped into D menu. So if choice equals quit the very last thing in the array I called quit I wanted to quit option just in case people want it out without doing anything. So if the choice is quit then I want you to echo program terminated and an exit one. So I just want you to exit out. Now if they choose something that's not quit so else if choice then I want you to do this I want you to print the choice meaning if I choose ZSH for example, print that entire line.  I only want the path right. So the fields are separated by spaces by default and also ZSH is a field the dash or the minus symbol that's a field and the path is a field. So I wanted all to print just the last field for us. Now what do I want it to do with that path to that config file well I want you to then run the command dollar sign DM editor that's the variable we set at the very top DM editor is basically my command to launch Emacs. So I want you to run Emacs path to the config and that really is the script like there's really nothing else to the script it was very quick and dirty is very easy if I wanted to I could scroll down here and go to my DWM config dot def dot H if I hit enter it launches it inside Emacs it looks like I got a maybe an error inside my config dot def dot H I'm not sure what that is let's try a different file go to my DWM Emacs config dot EL we'll launch that and there is that and we'll close that so very simple script but it solved a problem that I wanted to solve you know I just wanted a quick way to quickly open some of the common config files that I edit all the time so that was the purpose of this script why I named it DM comp for config let's check out one of the other little scripts that I've played around with here lately I created this one the other day called DM search years ago there was a really neat little script called surf roll that was created by Julian Assange that allowed you to search various search indices on the internet that script hasn't been updated in years and a lot of the options that are built into that script now are no longer working their links that are dead so I just wanted to create a simple little search script so the format of this is very similar to the last script I basically typically use the same kind of format I just did a variable at the top where I made a variable for the browser I want to use because this is going to be searching the web so I want to search the web obviously using a web browser the last script of course we needed a text editor because we were editing config files so I set DM browser equals the brave browser and then I created another array declare a for array and then I named the array once again options I'm not very original with these names and then once again I wanted to have three fields in each option the first field is just the name of the search engine that we're searching in this case Amazon and then the next field is again the dash or the minus sign and the third field is going to be the URL for the search engine and it needs to be a search URL minus the keyword that it searches for so if I was searching for I don't know distro tube this URL it would actually read out this so what I need is all of these URLs to be in the format or the it's the URL you know searching for a keyword or a query search and I need it to not include of course the keyword because when the keyword will constantly change we're going to add the keyword using d menu I've got all of these various search indices in this array again it's very easy this was not complicated the complicated part is going to each search engine and searching for something and getting the correct URL but scripting it is very very easy and then at the end I've got some while loops while kind of like if you know if then do this if this is true then do this while is while this is true do this and just keep doing it that that's what basically a while loop is I don't want to get way off into explaining that but it's not terribly different than what we saw in the last script and I have this here while engine we're going to have a variable called engine here in a minute do this and what I'm going to do is I created this variable engine list and what I want that to do is I wanted to print all of the options so every member of the options array I want you to once again pipe it into d menu with the same flags as the script we looked at before except the prompt is now choose search engine so if I do the key binding to run this script you say choose search engine and then once again every member of that options array which is the search engine hyphen and then the url now I don't really need the url displayed in this menu I could actually clean that up but it's fine being there for now the next thing I wanted to do was I wanted to take that search engine list which is once again this entire list here I wanted to awk the last field so that's what this is I want the last field which is the url and then I also wanted to awk the first field which is just the name of the engine because I'm going to use that in the next d menu prompt because I'm going to have this query down here query and then we're going to d menu and the prompt is going to say searching engine what is engine well engine is going to be taking the engine list and awking the first field so if I happen to choose youtube the next prompt is going to say searching youtube let me show you that so let me this is the first prompt where we're getting all the members of the array let me search for youtube I'm going to hit enter and the next prompt says searching youtube what am I searching youtube for I'm going to search for distro tube if I can type and you guys didn't see it but off camera here let me show you guys this it actually just searched in my brave browser for distro tube on youtube so that's just briefly what I've done with a couple of scripts here of course that was a search engine script you guys saw the previous script which was a script where I could edit config files that I edit on a regular basis let me show you just briefly one more that I've been working on I called this one dm red because it's for reddit it's going to be using d menu as a way to view reddit using a command line reddit viewer called radio which I think I did a video about radio a while back anyway this one gets a little more complicated because what are you going to do first you have to choose a subreddit from the options array here which I called not options this time subreddit underscore the list was what I named the array and then what happens when you choose one of these subreddits well I want you to give me a list of posts the latest I don't know 20 posts from that subreddit okay what happens when you select a post from that subreddit well I want to you just display the main message from that post I selected so I've already got three different things going on as far as you get d menu and then you choose something and then you get a second d menu you choose something and then you get a third d menu etc and I've this is very much a work in progress there's probably a lot more I'm eventually going to try to add to this thing but right now what I've got don't have a key binding for it yes I do you see the very first prompt choose a subreddit let me go down and I want to choose r slash command line and then I get a second d menu last 20 posts on r slash command line and I want to read actually I want to read that very first post it says the new shell a new type of shell I like the new shell let me read this post about it and if I hit enter it should have piped that message into a zenity dialogue box and the reason I'm piping it into a dialogue box is because by default you don't have text wrapping in d menu so you can't really read a lengthy post in d menu you have to pipe it into something else you know open it with a text editor or web browser whatever I just wanted it in a zenity dialogue box but it doesn't look like there was any text there let me try that once again and this time I'm going to go to the arch linux subreddit and I'm going to read we'll read the frequently asked questions from the arch subreddit okay and this is a more normal kind of post maybe there wasn't any text in the post I selected before but you can see it gets piped out into this zenity dialogue box which allows me to easily copy that text if I wanted to or you know if I don't want to do anything I could just cancel or I think escape also works if I escape out of it it exits out of that part of the script anyway I don't want to go over every single script that I had in this just very briefly on camera I will show you them in action so I had a scrot d menu script I called it dm scrot it actually uses maim maim as a command line screenshot utility and I gave this thing a ton of options as far as taking a scrot fullscreen or just the window I'm currently on or I could select a region I could copy to a clipboard I could take a screenshot of monitor one monitor two monitor three I could copy a screenshot of monitor one two three etc so there's a lot of options in this menu anyway I just hit enter and you know and I get a screenshot and the screenshots actually get posted to a screenshot folder in my home folder unless of course I choose one of the copy options and then it just copies that image to a clipboard that I could then use to paste into I don't know gimp or whatever it is I need to paste an image into the other ones I have I had this one here which is just a kill menu you see the prompt says search for process to kill it uses the standard ps command a standard linux command line utility to search for processes and if I happen to choose one it will ask me do I want to kill it for example maybe I want to kill let me see something safe to kill here Pycom and it's asking me do I really want to kill it it says kill and then the number of the process and then the name of the process Pycom if I hit yes it just runs the the kill command on Pycom but I do have the option to choose no to back out of it if it's a process I don't want to kill and another one I did was this one here which is just a simple shutdown menu so I can log out I can lock the screen reboot shutdown suspend quit so if I wanted to well I'll show you the lock screen that's a safe one to do while recording that locks the screen until I start typing my password and if I type my password correctly you know it unlocks that uses a suckless screen locker called s lock or slock I'm not exactly sure how it's pronounced I actually did a video about s lock a while back so if you guys are wanting to learn some shell scripting I strongly advise you to start playing around with something like d-menu or you could also do this with rofi you can pipe things into the rofi run launcher d-menu is very simple to use though that's why I recommend it it's just a fantastic program anyway but you know do what I did you know that search engine script was a problem I wanted to solve that's why I wrote that script find a problem that you want to solve and make it happen with some basic shell scripting and then piping it into d-menu now before I go I need to think a few special people I need to thank the producers of this episode absy delis gay blue Mitchell Allen a commie archv to 530 chuck david the other david dylan gregory louis paul scott west willy some other people I don't know I hope I get the names right I also want to thank each and every one of these ladies and gentlemen I would read the names but there's just too many darn names on that list the distro tube channel is sponsored by the community and if you'd like to support my work please look for distro tube over on patreon all right guys peace


So, we have kind of wrapped up the story with this Jordan canonical form. So, we started with our motivation being the solution of differential equations. And we saw that if you have a matrix which you can then diagonalize through a similarity transformation that is through some change of basis, then it is easier to solve the differential equation. And finally, all of this culminated in the fact that even if you cannot diagonalize it, you can still get it down to a very nice looking form, an upper triangular form and a very specific upper triangular form which is the Jordan canonical form where at most one super diagonal that is one term above the diagonal is nonzero and exactly equal to unity at most and everything else is still 0. So, it is still a very thin sort of a matrix around the diagonal and that is the best you can do right. There is also another form which we shall not have the time to delve into which is the rational canonical form right. So, I would urge you to do this as part of some self study it is not very difficult. Once you have wrapped your head around the notions the basic notions of how we went about this Jordan canonical form, the idea of minimal polynomials and the techniques we have employed. You can I would venture to say read this up on your own and understand a good part of it, but strictly speaking this is not going to be part of our syllabus. Just to complete the story I mentioned that just like you have the Jordan canonical form. Similarly, the rational canonical form is another very important canonical form into which we often want to cast our matrices into right. So, before we proceed because now we will only talk about few applications one or two in whatever times remaining in this course. If you have any queries about the Jordan canonical form what we discussed in the previous module please feel free to ask. If not I will just very quickly summarize. So, you have a matrix which we saw could be brought down to a block diagonal form such as this and thereafter we focused our attention on these block diagonal this individual block diagonals and we saw that these can be cast into some sort of a nice looking form where you have these Jordan blocks yeah. So, this generates a chain. So, this has an eigenvalue lambda i each of these a i i's has an eigenvalue lambda i only repeated d i times where d i is the geometric algebraic multiplicity of lambda i and this overall matrix that is a right. So, size is d i cross d i for each of these. So, this lambda i is the only eigenvalue of this fellow. Therefore, lambda i minus a i i turned out to be a nilpotent matrix and because we have this beautiful result that we proved that a nilpotent matrix can be cast into a form through some basis and we also give you a choice of the basis. Therefore, you can transform this object to have lambda i's at the diagonals the size of this largest such block it can be multiple in number by the way. So, if you have attempted one of the questions in the quiz yesterday you might have figured that out. So, it can have multiple blocks of the same size which is equal to the maximum size or it can have exactly one nonetheless the size of the largest block is exactly going to be equal to what the degree to which lambda i minus sorry lambda minus x or rather x minus lambda has to be raised in the minimal polynomial right. So, the degree of this fellow that is this f in the minimal polynomial this f is going to dictate the size of this it is f cross f the number of such Jordan blocks yeah is exactly going to be equal to the geometric multiplicity all right. So, how many blocks are there this is one this is two this is three like this. So, the number of blocks is equal to the geometric multiplicity and of course, the overall size this is di cross di. So, size of matrix a i i is equal to the algebraic multiplicity of lambda i right. So, you see already if you have geometric multiplicity equal to algebraic multiplicity what can you conclude well of course, the obvious right that it is going to be a diagonal block because geometric multiplicity dictates the number of blocks and if that is equal to the algebraic multiplicity then you have exactly di blocks in a di cross di matrix. So, each of them is just a diagonal entry right that is just another way of stating that the Jordan form a special case of the Jordan form is the diagonal form now right. The f the f is going to be the size of the largest Jordan block. So, that is what we said that if in the minimal polynomial every factor x minus lambda i has to be raised to a power 1 that is another equivalent condition for diagonalizability because then the size of the largest block is 1 right. So, then it has to be diagonalizable right. So, that is another equivalent condition for diagonalizability of a matrix in terms of the minimal polynomial. So, it is good to know because you never know when you have to prove a result which technique or which equivalent relation is going to be more handy. Of course, if you know how this works you will be able to prove one through the other you can also at this point you can go about proving the Cayley Hamilton theorem as well. So, when you want to prove the Cayley Hamilton theorem for a matrix just assume two things first not assume it is true we have shown that first thing is that the characteristic polynomial or the characteristic equation yeah it does not change with a change of basis. So, therefore, given a matrix you might as well transform it to a Jordan canonical form and then look at the corresponding characteristic equation the roots will be the same. Now, if you apply the Jordan canonical form as the argument x in the characteristic polynomial and replace suitably like with i's identities now it is an equation in an operator yeah then you will see that if you raise it to the power d i and the largest block is of size f i f i is strictly less than or equal to d i which is just another way of saying that the minimal polynomial divides the characteristic polynomial something that we used earlier, but now you can explicitly see how this works. So, each of those terms will go to 0 individually yeah because this is just got once here it will vanish away before you raise it to the power sufficiently large I mean at most if you raise it to the power d i it is guaranteed to vanish away yeah. So, that is exactly the argument behind this right. So, that is why this is also another way of proving the Cayley Hamilton theorem and none of this have we used any ideas from a determinants as you might notice right. We have from time to time gone on to use determinants to sort of compute the characteristic polynomial but that is more or less it because the determinants if you want to really define them there are a bunch of properties that it satisfies and that is how it comes in a rather non-intuitive way is what I feel which is why I would not bother with you know explicit definition of determinants and going along that route. So, with this we have come to sort of a culmination of the theoretical part or whatever tools and techniques we wanted to wanted to teach or pass on to you in this course. So, we will not start looking at few applications yes. Yes, a i i is for given lambda i this is sitting somewhere here. So, just this fellow becomes 0. Yes, this is a i i yeah this is just a i i this. So, I am just zooming in on this through a magnifying glass I am looking at this one of these objects is of size f which which is how many times it appears in the minimal polynomial overall minimal polynomial. So, the minimal polynomial of a i i is just this, but this will be a factor of the overall minimal polynomial of a that is what we have seen right. The overall minimal polynomial is a it is constituted by obtaining individual minimal polynomials of these blocks that is also something we have proved. So, you can just go back and trace your way back to all the way to see that this fits in nicely with the overall picture. Any square matrix any operator on a vector space it has to have a canonical representation right ok. So, today we will start looking at some objects which did not just appear out of some abstract ideas or thoughts, but from some problem some 400 years back maybe 400 or a little more than that. So, there was this bridge in it or a number of bridges over a river in a city called Konigsberg. Anyone has heard of this Konigsberg the name of the city. So, it looked something like this I am not a not an artist. So, I will not try to be very good at this drawing here. So, there was a river here and there were a couple of deltas like so ok. So, these are land masses in the middle of the river and there were a number of bridges I am told that in the modern day out of there are 7 bridges in all. So, this is a this is a city of Konigsberg there were 7 bridges out of which only 2 survive in the current day. I think it is currently in it was in Germany at that time it is currently in Russia yeah it is Kaliningrad is probably the current name of the place. So, the bridges were something like this I hope I have drawn 7 right yeah my arithmetic is correct. So, now interesting mathematical question arose. So, how many land masses are there 1, 2, 3, 4 right. So, these are the land masses so on. So, the question that intrigued people for a while was which is until the solution was proposed by a brilliant man right. So, the question was can we start from any one of these land masses traverse through all these bridges yeah and come back to the same point is it possible to do this all right and in order to solve this problem people thought and thought about several you know probably in combinatorial terms and in several other ways that they could think of, but no one could give a satisfactory answer as to why I mean people for after a while I am sure they felt it was impossible if not anything else they could just walk by and try different combinations and they probably realize the futility of it, but mathematicians as you might have already reasoned throughout this course are not happy with just carrying out some experiments multiple times and simulating stuff and believing it to be true just because someone isn't able to do it they want some concrete evidence in support of or against some proposition right. So, how do you explain to someone that it is indeed an impossible task to undertake the fact that you can never start out from take any land mass here start out from that land mass and then go about your business of traversing through a bridge yeah and then when you are in this land mass you again go through another bridge and then from that you have to take another bridge and so on and you have to traverse every bridge right. So, why is it impossible? So, you have any ideas why it could be impossible yes yes well. So, you can go about all the bridges, but you have to be back at the same point is it possible? So, can you can you do solve it if it is not once can you solve can you sort of traverse multiple times over the bridges and come back to the same point sorry keep walking and then keep walking multiple times yeah sure yes. So, it only makes sense when you have there restriction of only being able to traverse once across a bridge yeah why not why is it so definite okay graph theory, but that is the problem you see at that time graph theory did not exist. So, it is one of a problem such as this that actually prompted people to look for an abstraction.  So, in order to solve this problem you can actually look up Euler's paper although you will not understand the I mean sorry you will not understand the German that is written over there, but the point is that there is an abstract way of solving this. So, you name each of these land masses A, B, C and D. So, there are four land masses essentially that are separated by water bodies all right. So, let us say I represent the land mass A with just this one circle here and the land mass B with another circle here and the land mass C with another circle here and the land mass D with another circle here and let us say I will represent the bridges by drawing lines right. So, what can you say about between A and B? There are two bridges right right between B and C again two bridges between B and D this one bridge again between D and C this one bridge and between D and A this another bridge. It turns out this is actually a representation of this structure through a graph, but at the heart of it this graph is not what this picture depicts what do I mean by that? If I consider myself to be a Pablo Picasso of sorts I can sort of take this edge that is also this graph it is an abstract object at the end of the day this graph is nothing but these objects what are these objects. So, I define a graph in the following manner it is V which is a set of vertices or nodes that are these A, B, C and D and E which is a set of edges what are these set of edges can you guess what they are? How do you capture an edge? How do you describe an edge to vertices? So, it is basically if I were to put it down in mathematical terms it is contained inside a Cartesian product of V with itself. Of course, we can get rid of the ordering if this is symmetric I mean you can traverse this bridge any way you like. So, having a bridge between A and B is the same as having a bridge between B and A. So, this is an ordered pair of course every element in the edge set is an ordered pair, but in case that it is a symmetric relationship the ordering does not matter. So, you can kind of with an abuse of notation you can sort of get rid of this ordering and say that A, B is the same as B, A. But nonetheless an edge has a representation in terms of this. So, what is the maximum number of elements that you can have in this? Well clearly here you are having repetitions here. So, such graphs are not actually simple graphs they are called multi graphs. In general most often what you will encounter are simple graphs that is to say that between a pair of nodes or vertices if you have one edge that is it you cannot have multiple edges they are not identified as different that is still going to be identified as the same right. It is either there is an edge between them or there is no edge between them whether you have 20 edges or 20 billion edges between two nodes we do not care that is how a simple graph is defined. Now, this is not a simple graph well this is an abomination. So, let me just get back to the more conventional style yeah. So, this is a multi graph or a non-simple graph where multiple edges are allowed between the same pair of vertices sorry you do not need to write now here it is actually a little more complicated because every object can have a duplicate as well. So, you have to repeat it you have to repeat it yeah you have to repeat it you have to repeat the object and you have to specify in the structure construction of the set itself that when you are repeating it it should count towards its cardinality right normally if you say the set of fruits you would say oh you have apples you have oranges. So, how many kinds of fruits do you have that could be the cardinality of the set, but if you are specifically saying how many oranges do you have it means you are identifying every oranges different. So, with that kind of an understanding you have to say that well even though these are both oranges but when you are looking for sets of oranges then they are two in number right. So, the cardinality two they will they will add to the little contribute to the cardinality of the set if the even if there are repetitions. So, that is what happens in a multi graph, but we digress I mean. So, how is this construction going to help us in a more formal way to see that this problem is not solvable. So, here is the reasoning first thing is the reasoning for this problem. So, if you start from any point you have to exit through a bridge right. The moment you enter any of these landmasses you have to also exit through another bridge not the same bridge right which means what exactly unless you are at the first land mass or the last land mass you have to have an even number of bridges that have one of their ends on that particular land mass is it not. Every land mass here must have at least an even number of bridges connected to it otherwise you cannot go about this business without repetition is it not. So, in a language of graphs if I now translate it here what we are looking for is basically something called a degree. So, I am going to go about this very loosely because again graph theory or algebraic graph theory is not the primary goal of this course, but if you can absorb a bit of it it will probably be interesting to you. So, I am going about it informally these have all formal definitions ok. So, the degree of a vertex first thing I have defined is a graph set of vertices set of edges now comes the degree. So, what is the degree of a vertex the degree of a vertex is the number of edges that are incident on it again I have used a lot of terms incident on it pictorially speaking although again I repeat you should not think of graphs as mere pictorial objects, but pictorially speaking whenever there is an edge that is connecting a particular vertex to some other vertex then that edge is said to be incident on those two vertices which it connects alright. So, the degree of a vertex in a graph is exactly the number of edges that are incident on that particular vertex not necessarily we will assign something called an orientation later when we look at these objects through matrices we will get there shortly. For now let us not think about that we will we will describe that when it comes to that actually we will not deal with multigraphs I am just motivating this as a starting point for graph theory we will not deal with multigraphs we will deal with simple graphs later on. The point is that by whatever we have seen so far according to whatever we have seen so far what must the degree of every vertex be every vertex should have an even degree because the moment you are entering a land mass you have to leave it through some other bridge. So, the total number of bridges every time you enter you are allowed to enter the land mass multiple times, but you are not allowed to traverse the any bridge multiple times. So, you can come into the land mass as many times as you wish of course eventually you will run out of bridges, but if you have already run out of bridges when you are in the land mass that can only happen if you have an odd number of bridges right. Because every time if there is an even number every time you enter you will always find some way to escape a unique way to escape yeah. So, if you look at this graph here what can you say about the degrees of the vertices all of them have odd. In fact, if I did not ask you to come back to the same point, but visit every bridge there might still have been a solution why because not with this one of course then you can relax the condition that every vertex has to have an even degree. You can say that the starting vertex and the terminal vertex might afford to have an odd degree because you start from the starting vertex once and you have to come back necessarily as many times as you leave. So, the starting vertex can afford an odd degree the terminal vertex also can afford an odd degree, but when you fold back the starting vertex and the terminal vertex to be the same then it means that every vertex has to have an even degree and this is quite the opposite of that every vertex has an odd degree in fact right. So, this is how you establish that this Konigsberg bridge problem cannot be solved you cannot find a path that allows you to traverse every bridge once yeah and come back to your starting position right. In this case can could you have solved this problem if you for instance did not have to come back to the same point still no solution right because all of them have odd degrees you can at most afford any two of them having odd degrees in which case you start from one of them end at the other and traverse the others in between perhaps there is a path, but in this case there is absolutely no chance. So, even if I did not ask you to start from here and come back to it the problem would still not be solvable right. Now, in view of this people then wondered like is there a better way of capturing these objects. So, many years passed by and people made progress yes, not at not the end point and the starting point are not the same, not sure not, but you need not. You mean every vertex you have to visit only once that is a very difficult problem the starting for the vertex will never come back no. So, are you saying that you start from this A and you can come back to A, but you cannot terminate at A or are you saying that you cannot even come back to A. No, we can come back to A. Okay, you can come back to A, but you should not terminate at A. In that case is it not. The edges of the starting and the terminal vertices have to be odd then. Mandatory they have. Yeah, but again the total number of some of the degrees is still going to be even some of the degrees of all the vertices is still even because the terminal vertex and the starting vertex have odd degrees. The rest of them are even degrees. So, some of two odd numbers is even and some of the other even numbers is also even. So, that is the condition. So, the general condition I am glad you asked. So, the general condition is that the sum of the degrees of every vertex in this case also that is true because there happened to be like four of these fellers. So, four multiplied with any number. In this case they are all three, right? Oh, this is five. Okay, but still I think it's still even, right? 30009 plus 514. But still that doesn't solve the problem. Yeah, so you cannot have more than two. So, that's a complicated question because if I allow for things like self-loops because when you are allowing multigraphs you have to also account for the possibility of self-loops and that's when things start getting more interesting and also if you have directed graphs for example. So far we haven't considered any direction on these. If it's one way like a diode, diode allows current to flow in only one direction. So, if you have and it's not like some pigment of my imagination, I wish to actually cover a bit of something called a consensus like protocol by the end of today's lecture. But even before that, if you have a number of mobile robots, for example, which want to communicate with each other and decide where to go, it's not necessary that if robot one is listening to robot two, that robot two has to also listen to robot one. So, that sort of an information exchange is not bidirectional. So, there is an inherent asymmetry there. So, such interactions are also captured by graphs. In that case, if you have an edge connecting the nodes one and two, which are robots one and two, that will have to have a direction to specify who is listening to whom. If both were listening to each other, then you would just have an undirected edge and it wouldn't matter not. But when you are specifying that only one side is listening to the other, the other party isn't. Kind of yeah, it's something called a leader follower kind of thing.  That shouldn't happen in a democracy, but unfortunately, okay, that's a different story. Let's not get there. Okay, so now that people have pictures of these graphs and all, we want to understand if there's a better way to capture these relations without having to draw these pictures. Because pictures, there's only so much you can do with pictures, right? Let's say now you have 10 nodes, you might still be adventurous and draw it on the blackboard. Let's say there are 100 nodes, right? And you want to feed it to a computer. Do you want to draw a graphic image on a computer and feed it and sort of ask it to solve it for you? No, right? You want to feed some numbers, you want to capture these relations through arrays of numbers, if possible, and be able to discern or recover as much information about this graph or this networked system as you possibly can. So that is what spawned this area called algebraic graph theory. And as you shall see that it has a lot of applications of linear algebra, right? So again, this is going to be very informal sort of an approach, but I hope you'll be able to take something from this that you'll probably find useful at some time in your career later on. So algebraic graph theory. In order to capture these graphs through numbers, if possible through matrices as we shall sort of shortly see, this subject came into being, right? So I will again not motivate this through a bunch of definitions as I usually do for other topics. Rather, I'll draw figures and accompanying them, I'll write out some matrices and you'll be able to visualize how things work out, okay? So with every graph that you can draw, say for example, a graph like this, suppose this is a graph, it could mean anything. It could mean an electrical circuit, for instance, right? Where you know you do mesh analysis and node analysis, Kirchhoff's current law, Kirchhoff's voltage law, right? So this is basically an electrical circuit. If I tell you this is an electrical circuit with three loops and these are the nodes, you can sort of ground this node and I tell you what the impedances of these objects are, resistances, capacitors, inductors, and so on. You should be able to solve for the currents through any of these branches or any of these currents in any of these loops. That's an abstraction of an electrical circuit as well, right? So anyway, let's not be very specific here, but when you want to capture this graph, if you want to transmit this, do you think you're going to copy this picture and pass it to your friend? Okay, with four nodes, you can do this. When it gets bigger and bigger, you want to transmit this image to some friend sitting in some other part of the world through a chat. The friend is not going to wait for you to draw this on a piece of paper, you know, hundreds of nodes and edges and then you send it and the friend then because of what's this handwriting, they want some very crisp understanding of what graph you're talking about. How do you capture that? So one of the first objects that comes to mind is again starting with the degree. So let us call a matrix D as a degree matrix, okay? And what is this degree matrix? It's going to have a size equal to, what do you mean by this? This is the cardinality of the vertex set. So if there are four vertices here, this is going to be four cross four. So this degree matrix is going to be a diagonal matrix. Again, I'm not defining this, but I hope you get the idea of how this works. So it's a diagonal matrix. What's the degree of this? So let's immediately have to give numbers to this graph, to this vertices here. This is two, this is three and this is four. So the degree of one is three, the degree of two is three, the degree of three is three and the degree of four is also three. So it just so happens that in this case, it's just this diagonal matrix. So that's the degree matrix. Mind you, it need not be like this, like some multiple of identity. If I remove one of these edges here, for example, if I remove this edge, then the degree of one and degree of three would reduce to two each. So these numbers would have become two and two, right? So this is a degree matrix, right? The next important object is A, sorry? Which one? Sorry? Yeah. Yes. We will see. We will see. There is an interesting interplay. There's a reason why we are putting them in a diagonal and not as a vector. You're right. We could have just transmitted the same information through just four numbers. Why cook up four cross four? There is a reason. So then there's this next important object that is the adjacency matrix. So how is this adjacency matrix going to look like? This is also going to have the same size, all right? The same size. And actually we want D and A to be conformal for a reason. Because we'll see that writing them up as a difference leads to another important matrix for a graph, which is called the graph Laplacian matrix. So what is this adjacency matrix? Well, it's got to have zeros in the diagonals unless there are self-loops. So since we are dealing with simple graphs with no self-loops, the diagonal entries are going to be zero. What about the off diagonal entries? So if I denote the ijth entry of this adjacency as aij, aij is going to be either one or zero, depending on whether there is an edge connecting the ith vertex to the jth vertex or not. If there is an edge connecting the ith and the jth vertices, then aij is going to be one. If there is no edge connecting the ith to the jth vertex, then aij is going to be zero. That is how this adjacency is defined. And aii is going to be zero identically for a simple graph. So what about the 1, 2? Well, there's nothing really to see here, right? This one connects to this, this one connects to this, and this one connects to this. So it's going to be basically once everywhere. Is it not? I mean, this is what we call essentially a, you know anyone what this is called? It's a complete graph because it has all possible edges that you can see in the graph, right? So this is actually v cross v, every object is sitting inside it, yeah? So this is 1, 1, 1, 1, 1, 1, all right? So this is the adjacency matrix. Once we are done with this adjacency matrix, what we then define is a very important object called as the graph Laplacian. Already, if you feed the degree and the adjacency matrix to any friend of yours, just these two matrices, they already know what the graph is. You don't have to draw this figure, you see, right? And based on this degree and adjacency, you now have, so, d minus a, that is why we wanted to have that degree matrix in a diagonal form because it aids us in defining the so-called graph Laplacian. Why is this graph Laplacian important? Why is this important? You've already seen Laplace's equation many lectures back, maybe in the first lecture we discussed, first or second lecture when we took this area and split it up into measures, remember that Laplace's equation that nabla squared, you know, field theory, we discussed it. Just think about this. What is this Laplacian going to look like in this case? Is it not going to look like 3 minus 1, minus 1, minus 1, minus 1, 3, minus 1, minus 1, minus 1, minus 1, 3, minus 1, minus 1, minus 1, minus 3, right? This is what the graph Laplacian is going to look like. I wonder what is the significance of this graph Laplacian? If every vertex has a number associated with it, suppose this one has a number 7.1, this one has a number 10.1, this one has a number 8, this one has a number 6 and you stack it up as a vector, so that vector will look like 7.168 and 10.1. Are you following what I'm saying? So, suppose every one of these has a potential or a number, right? What do you think is going to happen if this is what I call as x, right? And I look at the object Lx. What is this going to be equal to? What is this equal to? The first entry is going to be 3 times x1, minus x2, minus x3, minus x4. Second entry is going to be minus x1, plus 3x2, minus x3, minus x4. If you distribute them, is it not like writing x1, minus x2, plus x1, minus x3, plus x1, minus x4, right?  So, these are my potentials at these different vertices. Now, this is the summation of the phi 1j's. This second entry is going to be the summation of phi 2j's. The third entry is going to be the summation of phi 3j's, where phi 1j is phi 1 minus phi j. You follow? And the fourth one is going to be summation phi 4j. So, in one shot, given node potentials, this Laplacian immediately converts it to what? It converts it to potentials across what are these numbers? These are absolute potentials with respect to some common frame of reference which is the earth. You follow? Some energy with respect to some base datum. Now, what I have here is the relation of that in terms of relative potentials. Phi 1j is phi 1 minus phi j that is 7.1 minus 6. So, these are relative potentials that are sitting over here, right? So, I have converted the variables which are the absolute values of these to sums of relative variables, right? The point is, can you solve for this now? That is, can you solve for these relative variables in terms of the absolutes? In order to understand that, we have to look at the property of this Laplacian, okay? So, we will do that in the next module, but I at least hope that you see why this Laplacian is such an important matrix. So, not so that we wanted to cook up the Laplacian using a artificially enlarged or bloated degree matrix when as your friend pointed out that the degree matrix could have just been depicted as a vector only instead of a diagonal matrix like this, right? Because this aided us in constructing the Laplacian which now gives us the relation of this load potential or the vertex potential to relative potentials or what we shall call as the edge potentials. Point is, if given the load potentials, can you solve for these edge potentials uniquely? Spoiler alert, in the next module we will see, you cannot do that unless you earth one of these nodes which should be no surprise really. From an electrical circuit perspective, if every point is a floating point and you only know Yeah, you have to at least fix up one of them as the base datum, right? So, we shall see that in the next module.


Hello and welcome to the session. Let's discuss the following question. It says using the properties of determinant show that the determinant a plus b, b plus c, c plus a, b plus c, c plus a, a plus b, c plus a, a plus b, b plus c is equal to the twice of the determinant a, b, c, b, c, a, c, a b.  We have to prove that this determinant is equal to this determinant. So, to prove this, we'll apply any row or column operation. So, here we'll apply the column operation. The c1 is equal to c1 plus c2 minus c3.    Now, again, we'll apply the column operation. So, c2 equal to c2 minus c1. So, we have the determinant twice of b, c, a. First column remains as it is and second column is c2 minus c1 that is b plus c minus b is c, c plus a minus c is a, a plus b minus a is b and the third column remains as it is. Again, we apply the column operation as c3 equal to c3 minus c2. So, we have twice of the determinant b, c, a, c, a, b.  Now, looking at what we have to prove, a, b, c should be the first column, b, c, a should be the second column and c, a, b should be the third column. So, we'll interchange the columns. So, a, b, c becomes the first column if we replace it by third one, right? So, c1 becomes c3 and c3 becomes c1. So, we have determinant a, b twice of a, b, c, c, a, b remains the second one only right now and this becomes the third one b, c, a and since we have interchanged the column, we have negative sign outside. Again, we need to have b, c, a, a as the second column and c, a, b as the third column. So, we'll interchange c2 by c3 and c3 by c2. So, c2 becomes c3 and c3 becomes c2. And again, since we are interchanging, we'll have negative sign but negative, negative becomes positive. So, we have twice of the determinant a, b, c. The second column becomes the third and third becomes the second. So, second is b, c, a, third is c, a, b. And this is what we had to prove. So, this completes the question and the session. Bye for now. Take care. Have a good day.


Good morning. Good morning, ladies and gentlemen. How are we feeling today? Happy thank you for joining us today, joining us at the National Archives. My name is Allison Seymour, and I'm so happy to be with you again this year. And again, thank you for joining us for a very special Fourth of July. The National Archives is, of course, the permanent home of the Declaration of Independence. For more than 40 years, the National Archives has hosted a ceremony on the Fourth of July to celebrate our independence. And this event is the kickoff for all of today's patriotic activities in our nation's capital. And if you're visiting, welcome to your nation's capital. After our ceremony, we urge you please stay right here and enjoy more live music followed by the National Independence Day Parade right here on Constitution Avenue. Or, man, it's hot. You can escape this heat and come inside your National Archives building to see the original Declaration of Independence and participate in our family activities. Now later this evening, the National Symphony Orchestra will present its annual concert, a Capitol Fourth right in front of the U.S. Capitol, and after the concert you can enjoy fireworks on our National Mall. Now you may have noticed our volunteers carrying big signs with today's hashtag and other social media information. The National Archives is on Twitter and on Instagram. And what it is is U.S. Nat Archives. Please share your Fourth of July using the hashtag archivesjuly4. Now after the ceremony, please don't miss our special Declaration of Independence signing booth. And following the ceremony will be set up inside the museum's Boeing Learning Center with other great family activities.  Most of you are already standing, but if you're not, please rise for the presentation of the colors by the United States Army Continental Color Guard followed by Ms. Crystal Moser singing the National Anthem. Oh say can you see, what so proudly, through the broad stripes and bright stars, the United States Army Old Guard Fife and Drum Corps. Now their uniforms are from the Roof Revolutionary War era, and so is their music. I am pleased to present specialist Nikolai Faduček to narrate their performance. Please join me in welcoming the Old Guard Fife and Drum Corps. Good morning, ladies and gentlemen. The United States Army Military District of Washington under the command of Brigadier General Omar Jones is proud to present the United States Army Old Guard Fife and Drum Corps. United States Infantry Regiment, the Old Guard, traces its lineage back to George Washington's original Continental Army and today serves as the Army's official escort to the President of the United States. In 1960, the Fife and Drum Corps was organized to participate in official ceremonies and to revive our country's musical heritage. From the days of the American Revolution through the 19th century, fives, drums, and bugles were vital to military order and discipline. Field musicians were used to issue commands during battle and to regulate the duty day, signaling when to rise, when to eat, and when the day ends. This morning's show paints a series of pictures from the life of a Continental Soldier musician. We open at the beginning of the duty day with a training scene. In the 18th century, signals like a tension and breakfast call would have sent the soldiers into action. Here, we begin with those signals and accompany their daily training with marching tunes including drums and guns and simple jasha. The soldiers of the United States Army Old Guard Fife and Drum Corps uniforms patterned after those of General Washington's Continental Army. In order to be easily identified, military musicians wore the reverse colors of the regiment to which they were assigned. At that time, American infantry soldiers wore blue coats with red facings. Thus, the musicians wore red coats with blue facings. Traditionally, the most skilled drummer was given the title of Drum Major and was chosen to lead the musicians. Today, the Drum Major who stands before you wears the light infantry cap and issues silent commands using the S-bond tune, an adapted 18th century weapon. At the end of the day, troops would often gather around the campfire to relax, and the musicians would provide entertainment. Picture yourselves in such a setting now as we feature the Fife and Bugle groups in a scene reminiscent of the soldier's respite following a challenging day. At a moment's notice, the soldier is summoned from camp, finding himself marching resolutely to the battlefield. As tensions mount, the musicians relay the commander's orders to the troops. Firing commences and the chaos builds to a fierce, percussive climax. We will now feature the United States Army Old Guard Fife and Drum Corps drum line in a battle feature. Bring the fallen soldiers lost in battle. We open our final scene with the mournful tune, Roslyn Castle. The moment is brief though as we transition to a celebration of life and close our show at the triumphal soldier's return during which the Corps will honor you with the stately and traditional troop step. On behalf of the Old Guard Commander, Colonel James J. Tewitt and the Fife and Drum Corps Commander, Chief Warrant Officer Five, Aaron Graf, it has been our pleasure performing for you today and we wish you all a happy Independence Day. Thank you Specialist Fiduczek and the Old Guard. Let's have another rousing round of applause. So this is the permanent home of the Declaration of Independence. That extraordinary piece of parchment is just one of billions of documents held in trust by the National Archives. The piece of paper, photographs, films in the holdings of the National Archives tell the story of democracy in these United States and the mission of the National Archives is to make these documents available to you, the American people. Now I'd like to introduce a very important person to whom our nation has entrusted the care of the Declaration of Independence. David Ferriero is the Archivist of the United States. David S. Ferriero was sworn in as the 10th Archivist of the United States in 2009. Previously, Mr. Ferriero served as the Andrew W. Mellon Director of New York Public Libraries. Before that, Mr. Ferriero served in top positions at two of the nation's major academic libraries, the Massachusetts Institute of Technology in Cambridge, Massachusetts and Duke University in Durham, North Carolina. Mr. Ferriero holds degrees from Northeastern University in Boston and the Simmons College of Library and Information Science also in Boston. He also served in the Navy as a hospital corpsman during the Vietnam War. Ladies and gentlemen, Mr. David Ferriero, Archivist of the United States. Thank you, Allison, and thanks for joining us this year as MC of our July 4th activities. Good morning. It's great to see you here to help us celebrate the 243rd anniversary of the Declaration of Independence. And special greetings to those of you in our presidential libraries around the country who are watching this via live stream. The 4th of July starts here at the National Archives. Through that door behind us is the original Declaration of Independence that seminal documents signed by our founding fathers enshrined in the rotunda of this building. Although a typeset version of the Declaration was printed on July 4th, 1776, the official government record on parchment was created and signed weeks later on August 2nd. I'm a lucky man. Every day I get to visit the Declaration and marvel at its very existence. The fact that it has survived for 240 years, given its history, is truly remarkable. This parchment has traveled extensively. While the National Archives opened in 1935, the Declaration did not arrive here until 1952. During the Revolutionary War, it traveled with Continental Congress and moved to Philadelphia, Baltimore, Philadelphia again, Lancaster, Pennsylvania for only a day, and then on to Princeton, New Jersey. At the end of the war in 1783, Congress was meeting in Annapolis, Maryland, then moved to Trenton, New Jersey. For five years from 1785 to 1790, the Declaration's home was in New York City. In 1789, the Secretary of State was directed to take control of all records, books, and papers created by the national government, and the Declaration went back to Philadelphia until this new federal city, the city of Washington, was built in 1800. When the British were burning Washington during the War of 1812, the Secretary of State James Monroe directed State Department clerks to get the important documents out of town. One of these clerks, Stephen Pleasanton, is my hero. He wrapped the Declaration and other precious documents in bags of linen, commandeered a wagon, and in the dead of night headed for Virginia with the records of the country just in the nick of time. The next day, the White House was burning, and the Declaration was safely hidden in an unused grist mill near Chain Bridge in Virginia, then moved to a private home in Leesburg until the war was over. During the 1800s, the Declaration was on exhibit for long periods of time at several locations in Washington where it was exposed to sunlight, fluctuating temperatures, smoke, and humidity, all of which took their toll on the document. Finally, officials took note of these effects of aging and wrapped the Declaration and stored it flat at the State Department. We rejoined the Constitution until 1921 when President Harding signed an order transferring both of these documents to the Library of Congress. Just before Pearl Harbor and the U.S. entrance into World War II, the Library sent the Declaration and the Constitution to Fort Knox for safekeeping where they remained until September 1944 when they were returned to the Library of Congress. Finally, these documents came to their rightful home here at the National Archives. The transfer occurred on December 13, 1952 with great pomp and circumstance and security as the newly encased Declaration of Independence was carried up these very steps with a military procession into the Rotunda. And the Declaration of Independence was safe until 2004 when the good treasure hunter, Nicholas Cage, cleverly stole it during a party in this building to protect it from the evil treasure hunter. And our national treasure was miraculously and circuitously restored to its rightful place and now poses the most often asked question in the Rotunda, can we see the back of the map? Is there a map on the back? And I can tell you for certain that the only thing on the back of the Declaration of Independence are the words of the original Declaration of Independence stated for July 1776. That's it. After the ceremony, I invite you to come inside our cool air conditioned building and see the Declaration of Independence the Constitution and the Bill of Rights. You can participate in family activities and check out our new exhibit Rightfully Hers which commemorates the centennial of the 19th Amendment and tells the story of women's struggles for voting rights as a critical step toward equal citizenship. The exhibit explores how American women across the spectrum of race, ethnicity and class advanced the cause of suffrage and follows the struggle for voting rights beyond 1920. Come inside and learn more. And a few reminders, you can share your pictures and stories from your 4th of July experience at the National Archives that US National Archives on Twitter and Instagram use the hashtag Archives July 4. You can also add your own John Hancock to the Declaration of Independence at our special signing booth inside the Boeing Learning Center here inside. And although we don't allow photography in the museum, we've made a special exception for our selfie station where you can snap a selfie in front of a special backdrop featuring our founding documents. So thanks for coming out today. The National Archives is the home of the official Declaration of Independence so really July 4 starts here. And now I'm honored to introduce our keynote speaker, Koki Roberts. Koki is a political commentator for ABC News and NPR and in her more than 40 years in broadcasting she has won countless awards including three Emmys. She's been inducted into the Broadcasting and Cable Hall of Fame and was cited by the American Women in Radio and Television as one of the 50 greatest women in the history of broadcasting. In addition to her reporting, Roberts has written six New York Times bestsellers most dealing with the roles of women in US history. Koki holds more than 25 honorary degrees and serves on the boards of several non-profit institutions. In 2008 the Library of Congress named her a living legend, one of the very few Americans to have attained that honor. Koki is also vice president of the National Archives Foundation Board and we are pleased she could join us today for our 4th of July celebration. Please welcome Koki Roberts. Happy 4th everybody. And it's wonderful to be here celebrating the 4th of July. Of course it was that glorious day in 1776 when the 13 colonies declared their independence as grand as it was it came a little late for one patriot. Let us separate. They are unworthy to be our brethren and let us pray to the almighty that to blast their councils and to bring not to all their devices. That was December of 1775 when Abigail Adams was ready to smite the British and she wanted to do it for a good reason. The Redcoats were attacking her and her children while John was off debating and dining in Philadelphia and at one point he wrote to her and said if it gets really dangerous take our children and fly to the woods. Thank you John. By March of 1776 Abigail had totally run out of patience. I long to hear that you've declared an independency. And what would that independency look like? She wondered. In the new code of laws which I suppose will be necessary for you to make I desire you would remember the ladies. Maybe the most famous words ever written by an American woman. What did she mean? She's not telling us today. Some historians thought she was kidding. I certainly don't. Abigail Adams knew she was being left out of much of the promise of the new nation. And she argued that her devotion to America despite her exclusion made her a better patriot than the men who stood to reap its benefits. Deprived of a voice in legislation obliged to submit to laws which are imposed upon us is this not sufficient to make us completely indifferent to the public welfare? Yet all history in every age there are instances of patriotic virtue in the female sex which considering our situation equals the most patriotic and heroic of yours. Indeed. So slowly the women of America took up the cause of having a voice in legislation through the vote. Two years after Abigail Adams died in 1818 Susan B. Anthony was born in Adams, Massachusetts. She went on to form her famous partnership with Elizabeth Katie Stanton who at Seneca Falls in 1848 wrote the Declaration of Sentiments a declaration based entirely on the one you will hear shortly today but with some basic alterations and those alterations some of them will be read appropriately by the next generation my daughter Rebecca Roberts. We hold these truths to be self-evident that all men and women are created equal. As the colonists charged the British with their litany of abuses so did the women charge the men. He has never permitted her to exercise her inalienable right to the elective franchise. He has compelled her to submit to laws in the formation of which she had no voice. He has withheld from her rights which are given to the most ignorant and degraded men, both natives and foreigners having deprived her of this first right of a citizen, the elective franchise thereby leaving her without representation in the halls of legislation he has oppressed her on all sides. He has made her if married in the eyes of the law civilly dead. He has taken from her all right in property even to the wages she earns. And on and on and on and finally concluding. And now in view of this entire disenfranchisement of one half of the people of this country their social and religious degradation in view of the unjust laws above mentioned and because women do feel themselves aggrieved, oppressed and fraudulently deprived of their most sacred rights we insist that they have immediate admission to all the rights and privileges which belong to them as citizens of the United States. Huzzah! Sixty-eight women and thirty-two men signed the document including of course Elizabeth Katie Stanton Huzzah! Lucretia Mott and Frederick Douglass will be another seventy-plus years before the elected representatives of the people of women what was rightfully ours as citizens the right to vote. The story of that decades long struggle of women marching bravely in their white purple and gold that story is ably and amusingly told inside these halls in the rightfully hers exhibition in the Lawrence O'Brien Gallery. So please come in and see it as you enjoy this Independence Day in the knowledge that our Union while still not perfect continues to strive toward that end. And Abigail Adams I am rightfully honored. Thank you very much. Thank you so much. May we hear it once again for Koki Roberts. I'm happy to introduce to you a very distinguished group of people who will read the Declaration of Independence. Our first three readers are General George Washington Mr. John Hancock and Mrs. Abigail Adams. Next to read the grievances against King George III we will have three of the leaders of the Second Continental Congress Mr. Thomas Jefferson Mr. John Adams and Dr. Benjamin Franklin. These three gentlemen know the words of the Declaration better than anyone else. All three served on the committee to draft the Declaration and Mr. Jefferson was the primary author. And to read the names of the 56 signers of the Declaration we are proud to have Edward Ned Hector of the Third Pennsylvania Artillery Company Free Black Colonial Soldier Patriot and Hero. And finally we will have some audience participation just as our colonial forefathers would have done. And our special guests read the grievances as they do so against King George. Watch out for our town crier assisted by our volunteers. They're holding the signs. You can get a preview right there. Holding the signs to tell us when we should express our displeasure with a hearty boo ladies and gentlemen the Declaration of Independence. In Congress July 4th 1776 the unanimous declaration of the 13 United States of America. When in the course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth the separate and equal station to which the laws of nature and of nature's God entitle them a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation. We hold these truths to be self evident that all men are created equal that they are endowed by their creator with certain unalienable rights and that among these are life, liberty and the pursuit of happiness. That to secure these rights governments are instituted among men deriving their just powers from the consent of the governed and that whenever any form of government becomes destructive of these ends it is the right of the people to alter or abolish it and to institute new government laying its foundation on such principles and organizing its powers in such form that to them shall seem most likely to affect their safety and happiness. Prudence indeed will dictate that governments long established should not be changed for light and transient causes and accordingly all experience have soon that mankind are more disposed to suffer while evils are sufferable than to write themselves by abolishing the forms to which they are accustomed but when a long train of abuses and usurpations pursuing invariably the same object in visions that designed to reduce them under absolute despotism it is their right it is their duty to throw off and to provide new guards for their future security such has been the patient sufferance of these colonies and such is now the necessity which constrains them to alter their former systems of government the history of the present king of Great Britain is a history of repeated injuries and usurpations all having direct object the establishment of an absolute tyranny over these states to prove this let facts be submitted to a candid world used his assent to laws the most wholesome and necessary for the public good he has forbidden his governors to pass laws of immediate impressing importance unless suspended in their operations till his assent should be obtained and when so suspended he has utterly neglected to attend to them he has refused to pass other laws for the accommodation of large districts of people unless those people would relinquish the right of representation in the legislature a right inestimable to them and formidable to tyrants only down he has called together legislative bodies at places unusual uncomfortable and distant from the depository of their public records for the sole purpose of fatiguing them into compliance with his measures he has repeatedly dissolved representative houses for opposing with manly firmness his invasions on the rights of the people he has refused for a long time after such dissolutions to cause others to be elected whereby the legislative powers incapable of annihilation have returned to the people at large for their exercise the state remaining in the meantime exposed to all the dangers of invasion from without and confusions within he has endeavored to prevent the population of these states for that purpose obstructing the laws for naturalization of foreigners refusing to pass to encourage their migrations hither and raising the conditions of new appropriations of lands he has obstructed the administration of justice by refusing his assent to laws for establishing judiciary powers this may judge his dependent on his will alone for the tenure of their offices and the amount of payment of their salaries he has erected a multitude of new offices and sent hither swarms of officers to harass our people and eat out their substance he has kept among us in times of peace standing armies without the consent of our legislatures effected to render the military independent of and superior to the civil power out of my way he has combined with others to subject us to a jurisdiction foreign to our constitution and unacknowledged by our laws giving his assent to their acts of pretended legislation for quartering large bodies of armed troops among us for protecting them by a mock trial from punishment for any murders which they should commit on the inhabitants of these states for cutting off our trade with all parts of the world for imposing taxes on us without our consent for depriving us in many cases of the benefits of trial by jury for transporting us beyond seas to be tried for pretended offenses for abolishing the free system of English laws in a neighboring province establishing therein establishing therein an arbitrary government and enlarging its boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule into these colonies for taking away our charters abolishing our most valuable laws and altering fundamentally the forms of our governments for suspending our legislatures and declaring themselves invested with the power to legislate for us in all cases whatsoever. He has abdicated government here by declaring us with his protection and waging war against us he has plundered our seas ravaged our coasts our towns and destroyed the lives of our people He is at this time transporting large armies of foreign mercenaries to complete the works of death and tyranny already begun with circumstances of cruelty and perfidy scarcely paralleled in the most barbarous ages and totally unworthy the head of a civilized nation. He has constrained our fellow citizens taken captive on the high seas to bear arms against their country to become the executioners of their friends and brethren to hold themselves by their hands He has excited domestic insurrections amongst us and has endeavored to bring on the inhabitants of our frontiers the merciless Indian savages whose known rule of warfare is an undistinguished destruction of all ages sexes and conditions. Mr. Adams In every stage of these oppressions we have petitioned for redress in the most humble terms our repeated petitions have been answered only by repeated injury a prince whose character is thus marked by every act which may define a tyrant is unfit to be the ruler of a free people Nor have we been wanting in our attentions to our British brethren We have warned them from time to time of attempts by their legislature to extend an unwarrantable jurisdiction over us. We have reminded them of their circumstances of emigration and settlement here We have appealed to their native justice and magnanimity and we have conjured them by the ties of our common kindred to disavow these usurpations which would inevitably interrupt our connections and our correspondence They too have been deaf to the voice of justice and consanguinity We must therefore acquiesce the necessity which denounces our separation and as we hold the rest of mankind enemies in war in peace, friends We therefore the representatives of the United States of America in general congress assembled appealing to the supreme judge of the world for the rectitude of our intentions do in the name and by the authority of the good people of these colonies solemnly publish and declare that these united colonies are and of right ought to be free and independent states Yes Yes are absolved from all allegiance to the British crown and that all political connection between them and the state of Great Britain is and ought to be totally dissolved and that as free and independent states they have full power to levy war conclude peace, contract alliances, establish commerce and to do all other acts and things which independent states may of right do And for the support of this declaration with a firm reliance on the protection of the divine providence we humbly pledge to each other our lives, our fortunes and our sacred arm honor We'll now read the names of the colonies and the signers of the declaration Like the colonists rather we will show our approval by shouting Huzzah So once again watch for the town crier to assisted by our volunteers holding the signs to show when you should shout So after Private Hector reads all the names from each state let's Huzzah our approval But first let's practice with a hearty Huzzah on the count of three One, two, for Private Hector to read all of the names from each state and then we're going to shout our approval with a Huzzah and now the names of the signers of the declaration of independence Which one of you out here would be one that signed your own people were willing to sign their own death warrant Attend now as I read their names The Honorable President of the Continental Congress Hopkinson and this document is the Secretary of the Continental Congress telling the sign this document Let us give them We have the program finale I want to tell you about some of the activities that we have inside the National Archives building today The building closes at 7 p.m. Don't miss your chance to see the Declaration of Independence the Constitution, the Bill of Rights and the Magna Carta We also will have a special hands-on July 4 family activities in the Boeing Learning Center until 4 p.m. We're going to stop by the National Archives store tent for exclusive Independence Day products that support educational outreach and events just like this at the National Archives I'd also like to thank the people who helped make this year's 4th of July celebration possible The National Archives Foundation and to long time sponsors of this great event John Hancock Financial and Dykema along with the Hearst Foundations for their major support for the historical theater and our founding fathers Thomas Jefferson John Adams and Benjamin Franklin and our representative to the Continental Army Private Ned Hector our guest General George Washington John Hancock Abigail Adams John Dunlap our town crier the United States Army Continental Color Guard and Old Guard Fife and Drum Corps retired Master Sergeant Caleb Green and the Experience Band and Show and of course we wouldn't have this celebration without the hard work of the staff and volunteers of the National Archives and I also want to thank you all of you for being with us today to commemorate the 243rd anniversary of our Declaration of Independence It's been my pleasure to be with you today The National Independence Day Parade starts at 1145 right after this ceremony but before the parade starts the Experience Band and Show will join us on stage for more live music I wish you all a wonderful 4th of July and I hope you'll stay after our finale and take part in our activities this afternoon and share your 4th of July experience on social media with the hashtag Archives July 4 and now please remain seated as we welcome retired Master Sergeant Caleb Green who will close our program with America The Beautiful followed by a special surprise Happy 4th of July


Hey everyone, Drew with GeoArm and I am back to talk to you about the LTE-X and the LTE-M-X series communicators by Residio. So these are going to be super easy to install, it's six wires total and the device comes with a wiring harness already for it. So what we're going to do first here is we'll get the device opened up. As you can see there's a screw here that you're going to need to back out just a little bit. It doesn't come all the way out. Once you've gotten that backed out you just pop it open like this, just opens right up. What we're going to be doing is we're going to be wiring into this little slot over here on the side. So this thing just snaps in place as you can see there are little wiring harness that they've included for us here. So we're going to go ahead and get that snapped in.   Sorry guys, I just want you to be able to see what I'm doing here. So I'm going to go with my connections to the keypad bus. Now remember prior to doing anything on this panel you need to make sure this thing is completely powered down. Unplug the backup battery, unplug the power supply. There should be no power at all going to the system. Once you've confirmed that we're going to go ahead and wire it into terminals four, five, six and seven just like a keypad. So we're going to take the black wire that's going to go to terminal number four. There will be other wires in here as I said this is the keypad bus. So anything that requires aux power or anything that requires data transmission will be going to these terminals that we're wiring into. So black wire to four, red wire to five. There will be other wires going in there of course. Then we're going to go with the green wire to terminal number six. Get that locked in place. Once again there will be wires in these slots just to reiterate that. And finally the yellow wire we're going to go to number seven and get that locked in place. Okay once you've made those connections this device is wired back to the panel and 100% ready to be activated. So what you need to do now is you would get your cover placed back on, screwed down in place. Obviously I can't do that because I was sloppy and didn't feed the wires out the back. But that's all good.  At this point you can power your panel up. Make sure you get the MAC and the MAC CRC from inside by the way. And then give us a call for activation. If you guys have any questions or any comments please leave them below. Take care. Make sure to subscribe to our YouTube page and click the Show More tab underneath the video where you can view valuable links pertaining to this product, similar how-to videos, and our low-cost no-contract alarm monitoring services.