I want to compare and contrast two different types of back squats today.  There are two different types, right? So I kind of described both of them there. If I put the bar really high on my shoulders, we'll call this a high bar squat. So the leverage away from my back and away from my hip gets longer, because I'm up here, I'm not putting the bar down here, I'm putting it up here on my trap muscles, right? My upper, upper trap muscles. So as I bend over, that torque from the weight gets amplified, and the whole point of lifting and biomechanics and coaching is to minimize some of that when you're trying to get stronger, or maybe even maximize that disadvantage, that torque, to allow you to use a really light weight for something to build muscle, right? So the difference is I can do maybe 25s for my lateral raises if I go like this, but I can only do 15s if I keep my arms straight. The lever is longer away from my body. So the same principle applies to back squatting, high bar back squatting, right? So I have this longer lever, and I feel more, gets amplified. So I cannot bend over more, because that puts me at too much of a disadvantage. Therefore, a high bar squat, we need to try to control by being more upright. General rule is I want the back angle and my shin angle to be parallel, okay? Hopefully I'm doing that in our demo. This is definitely wrong. You see how my shins go forward like this and my back is upright, and then this is definitely wrong for that. Contrast that with a low bar squat. So with the low bar, I just put it on my rear delt area and I crank my shoulders back. Like I'll grab the bar and I use that to just crank my shoulders back. The bar sits really low, and so the soft tissues of my shoulder joint actually start supporting the weight. It starts to hold the bar, and I have to bend over so I don't just rip my arms right off my body. And that gets my back underneath the weight a little bit more. And then when I squat down, I need to bend over even more so that I don't lose control, right? So we call this low bar squat a hip dominant squat. Most of my motion is occurring at my hip, getting extra hip motion, less knee motion. In any squat, I need the bar to stay over the foot, like front of the ankle area. That's what tells me that you have your balance. That's what tells me that you're not shifting forward when you squat. So if you're filming yourself, get a good like totally 90 degree angle and look for it. Now, okay, compare and contrast. I don't really give people the low bar back squat very often because I think it's overrated. I used to do it, but if I'm bending over more, it's hard for me to get this hip mobility, which people are already limited in. And if I'm doing it for the sake of powerlifting, it's really hard to hit depth. Because we define depth as the hip crease coming below the knee. So if I drop straight down like a high bar squat, that happens much easier than if I'm bending over a lot like this, right?  It's not even bent that much and my hip is not below my knee level. So consider that. A lot of people start with their low bar squat. A lot of, you know, professional powerlifters or experienced powerlifters will use a low bar squat because they're wearing extra supportive canvas around their hips. They're wearing a squat suit. They're wearing squat briefs, whatever. And they can bend back and they can keep their tibia vertical. They can keep their shin vertical and still push their butt way back. That really allows them to use those hip muscles. But they're also getting a lot of support out of the suits that they're wearing. So if you're not wearing a suit, consider being more upright. That's pretty much the variation that I'm using, or that's the variation that I'm pretty much using for most or all of my clients. If you have some knee problems, I'll let you bend over more and not bend your knee quite as much. But I still want you to be able to demonstrate that you can squat down and bend your knee without it hurting. So those are just some random thoughts on comparing contrast to the knee dominant, hip dominant, high bar versus low bar squatting.


All right folks good afternoon and welcome on back here this Tuesday, June 28th Shortly after 2 30 p.m. Eastern Time markets are breaking lower here heading into this afternoon meeting great to see Later Michael Norman, and I'll tell you what folks for all this just rejoining us here Otherwise great to see everybody especially those of us on social media Facebook live or YouTube joining us today, but We said it earlier. I'll repeat it for all of us in social right now, but you know, I love days like today I love markets are tanking. I love it Why because this proves our point as day traders here at least inside the cyber group trading room To a take because although the markets are tanking and breaking the lower right now. We're beginning to AGRX at least from earlier today and even just before heading into this meeting at least You know it's been a really nice runner So you can't tell me that for those of us they can't short or you know Look to follow, you know the market on the way down at least you know if you're trading Ira or cash only It's to say that Hey This proves, you know the fact that you can make money you got to be there at the right place the right time You got to work together as a team whether it's with a larger group of people or a smaller group of people like us inside The live trading room and when I say smaller, there's like a hundred of us inside here But comparing that's like some like the bigger trading rooms that you may know It's like there's not as much of an advantage there like here is like so primed to just be inside the trading room See a lot of our experienced traders like Gene, Ron, Michael, Leda You know actually all those that just chatted back to me right there You know those are some of our longtime students who've been around the block with us Norman too and some of our more recent students But very you know successful as they've been proven to be inside the trading room like Robert or John or Steve So it's to say you know, hey, there's a lot of opportunity, but you can't do it on your own You got to work with a group, you know smaller group perhaps like we have here So it's to say AGRX right now. I don't like the shake, right? I mean the shake back down off these highs is pretty violent Leads me to think that this might look to kind of just pull back further here heading into the afternoon So I'm not fully committed to it here at this point actually yesterday afternoon. We had a good list It was actually very unfortunate. Nothing really was moving too. Well, you know granted markets for beginning to pull back then But like AMC was flat You know CLVS didn't make the move that we wanted it to make SRK and we actually had a shutout on the watch list yesterday afternoon So, you know, this could be in play. Maybe this does build support later on but Not fully committed to it just yet. So we don't have class this afternoon folks That's for tomorrow for all this live inside the trading room any of our gold platinum or diamond students like Michael or Leda perhaps there Huh, you know, if I was to will be doing the phase three stock horse class tomorrow But you know, let's still go right from top to bottom. Let's see what we could do You know here heading into the afternoon the AGRX is a maybe We got a bunch of these cheapies below a dollar here on the gainer side like tour HTGM ENDP, let's skip over them for right now now with that in mind KZR What a dud this has been unless if you were able to short it's hard to borrow on trade station I didn't care to check to get shares and maybe that You know, it was to my disadvantage But you know ended up dropping off as soon as the market opened and I had a couple of support levels that I was hoping to see hold And I'm not just relying on hope I'm not currently in the street as you could see but I did get chopped up just a little bit earlier in the afternoon I had a pretty good morning not as good as yesterday. Perhaps yesterday was like incredible to me Today is alright. I'm still up But I know I'm not gonna really hit my you know goal at least, you know for the afternoon Actually, I shouldn't say that maybe we'll see but you know if I don't hit it It's alright, but I did get chopped up earlier which gave back some of the profit I made from this morning on KZR I was looking for support to hold off of 9 and then also I was writing in the trading room like a FIB level I had off of the 873 or 877 something around there and you could see there It was trying it was trying here and then once it ended up breaking back below that FIB line I took my third loss in a row on it tiny losses, but they add up and then from there I stopped trading it and thank thank God I did but Right now. I mean don't hold your breath waiting for a squeeze back up today I mean there's not really a clear support level on this in my opinion at least until 8 and then you know Otherwise, I was really lining up like 750 so this might have a way more Downside left before a potential bounce. So Again, not fully sold on this KZR Gray from earlier today a little pop-up from this morning, but not a whole lot to it after that, right? S-t-r-o look at this thing go and I'll be saying that for that to write But nice little pop from this morning actually this thing had a bunch of activity pre-market this morning like early early on So, you know ended up like moving up as high as like six or up as high as like 730ish you can kind of call that now from there it ended up dropping off and took a while for this You know pop to even come to fruition, but you know right now you hope to see a lot more of this to come So no strobe here. I'll put on our watch list just to respect this pop But also on the flip side of it. Actually, I know that the HERX is hard to borrow KZR is hard to borrow for me But this one I know is short of all so let's say if this is like a false pop like a fake pop You're coming up at least I know I could short it you know check check with your broker to see if you can get the shares if the if it's a false break at At least but uh, you know I'll respect the pop the breakout here right now and strobe this on our list looks good Got my no-pads that are right this down on like a browser window here. So if I delete it, I'll get pretty close Let's see it all so we got here in the meantime CRNT this is like more of like a level one stock level one or two Which you know for a lot of our newly enrolled students It's pretty good, but right now specifically right now this time here. It's not doing anything So, you know, it could be a good short should we see more selling and should this dip down a little bit more, but See what also got here the same to be said on we Joe I'm sure I haven't checked in on we Joe in a little bit but from a pre-market this morning It made a nice move to begin but then ended up dipping off heading into the open flattened out and You know, I was interested but then it teased me So I didn't trade this at all, but you know, I ended up moving away from this once the market did open and then From there didn't really look at it dropped off down to like 125 then bounced back up, I guess here But otherwise not a whole lot to it right now Not gonna find a whole lot on the gainer side folks, right? We always like to say that on days like today How about you VXY see sqqq up here, you know, of course the inverse ETFs or the VIX ETFs nonetheless will be up so this year is actually sqqq so inversely follows Nasdaq 100 or the Q's ETF, you know, obviously this is at the highs here So I assume UV XY to be doing the same I'll likely like put the spotlight on UV XY, but sqqqq I know a bunch of us trade inside our live trading room here So, you know for right now at the markets dropping off will focus it on one of these All right, let's see what else we got here probably not a whole lot left, right on the gainer side Just quickly click on NCT Y from earlier and not a whole lot happening right now AERC I see is up like six percent still on blue aprons. So, you know, there's a couple more left I do want to check out, you know, a couple of stocks like these made some good moves from earlier this morning or afternoon So AERC at least you could see here ended up making a nice pop if after the open But what you're seeing here is exactly why I call the stock a gamble stock, right? I think I said that yesterday afternoon this time of the day This is not like a casino stock, but this is like you're risking your life on the stock So, you know, if you didn't realize that before today, I hope this is a good reminder, right? Lot of these small cap low float stocks. They'll make these big drop-offs like this. It's you know, really dangerous to swing trade Same with blue apron. Unfortunately. I haven't checked in on this one since the lower high It was moving back up to four, but you know, I expected four to hold at first But that's a nasty drop. So I think blue apron is more of a Mid cap flow maybe loaded mid cap, but not as low as like, you know, the others these pop it drops But no blue apron right now. I mean, hey, just I'm sure it's tradable, but given the drop-off that we had here I'm not as interested in it right now. So All right, let's see what else we got here on the loser's side You know, it's interesting Ly T or yeah, Ly T here this thing got clipped I have no idea what happened here at least across the afternoon as to why it's down like 84 percent It was down a lot more from earlier. I was getting close to like 90 percent at one point But you know stock took a huge hit from the market open got halted probably like, you know 20 times here That halts it to oblivion. You could see just every little white horizontal dash on the one-minute chart Those are all halts so With that I took a trade on this and this gave me a little money back at least from earlier after I got clipped on a KZR So Fortunately, I got in this at the right time and given the how thin the book is right now This is definitely a bit of a gamble stock, you know But given how much it dropped off you hope to see some form of the dead cat bounce So I ended up attending to this trade like right before I ended up leaving the office here for the day I'm working for my home office right now and ended up seeing it begin to squeeze back up I wanted it to drop the lower down to 480. I had a order out there just to try and catch it at 480 You know it's pretty low even from them from where it bottomed out at but you know ended up squeezing back up And then once it ended up getting halted going up I ended up jump I ended up jumping it off of 630 and it took a little while for it to break But fortunately I got in like kind of towards the tail end here as it was beginning to break back over 630 And with that ended up leading to a pretty nice run Granted it wasn't on like a full share count But you know this is the type of stock. Hey given how much it dropped from like 40 or 50 bucks All the way down at near 5 Come on now. So, you know if it's not gonna break any lower. There's only one other way. It's gonna go, right? So I'm not in this for like a 5 cent profit 10 15 cent profit I'm looking to make like a dollar or two at that So it ended up squeezing up pretty nicely at first had a one shake to it Squeezed up pretty nicely and then I ended up getting out just under 750 and then moved up a lot more afterwards I knew it was on a steady trend, but the thing with these types of stocks I mean, you know, we just said it before an AERC seemed to be set on this one You know just on a short squeeze on a dead cap bounce, whatever the hell we're calling this It's just to say when the volume dies off So does the stock this thing ended up dropping off a lot faster compared to you know the pace it moved up in So, you know, you need to be very careful and you have to make sure that you get in at a very good time and price and say You're stop and you know, that's easy to say. I'm sure I'm sure that's easy to say, but if you know your levels then You know it gives you a pretty good edge right level three level four gives you a good ability for that So actually how about this? I had this up prepped up on the other screen ready to go, but You know, I mean I get lost in my own flow here and I Go off this so I can see the LYT trade I did bring up book map for all this year during this meeting. I wanted to do this So now this is where it ended up beginning to squeeze up and over time 630 was a pretty big level to watch here, right? A lot of pent up volume You know getting filled around 625 630 and with that just once it broke the iceberg order I ended up jump jumping in shortly after and it led to a nice run So from there, you know, that's where I got my squeeze but across the afternoon right now You know, I'll put this on our watch list given how much it's still down No, perhaps there could still be room for this to you know make one more run But when the volume dies off this thing will tank and we'll get halter going down again And you know, you don't want to get caught on that side of the trade So LYT I'll put on our list here so far. We only have three set three symbols on our list one of them's ETF So, you know, unless of the markets dead cat bounce altogether here You know, we got to find a lot more from the loser side that is a good short that could you know follow the market here going down CVNA mark if he's still here I know he dipped out. He made his days pay earlier at earlier actually on the sqqq trade but a CV at CVNA he's been a big fan of lately, you know, this stock is shortable It's down big it just dropped off to make a new low earlier bottoms out off of 25 perhaps here But still very active. So, you know what? I like this one for right now CVNA What a break in between here folks one second. It's been a long week of talking already him It's like a class week. So pretty interesting But uh, well for Fausto it is not me, but nonetheless we go real a little cheap here on the way down even if it is shortable I Not really a fan of shorting like a two dollar stock three dollar stock And so unless it was dropping off really fast and making a big move then I'm not gonna have as much business with it FNG you here. I think it's an ETF. It could be wrong. Yeah, it is ETN. All right, folks, let me know if there's anything else that looks good up or down type it in the chaplain here Let me know got my neo trade. I was in on earlier right off of 2255 for all of our students and members inside the live trading room We had traders talk earlier today. You heard me talk about it. I literally went over this trade and talked about from last week We had like a 10 million share 9.1 million share volume spike at 2255 So, you know from earlier today, this was my bread and butter stack and I ended up dropping shorting this from like 2317 but I'm ended up dropping off greatly and I took most meat off the bone there But from that point once it rebounded I ended up going short right from 2255 2254 is my price and from there just pretty simple short, right? So it just goes to show like what you hear and traders talk what we talk about as a group even The questions that we answer as a group it pays off, right? So that recording is actually already on the student portal I kind of lucked up last week and I ended up forgetting to put it up for a you know that Tuesday Tuesday So I had to put up a couple days after so that was my fault and up I wanted to make it up to you and it's already up on the dashboard right now the student portal So no for anyone that missed out on our weekly workshop earlier today traders talk You could actually watch that just go right to the homepage All right So for right now Nio right now this thing is down like two and a half percent not a whole lot And it's beginning to inch back up a little bit here So, you know, I'm not really too interested in it right now. I mean from the morning I was but not as much right now AMC hey, we ended up calling us out yesterday early on we were really early to the punch on this trade yesterday Thankfully it ran up greatly at the time and you know for right now It dropped off after the market opened up, but it seemed to be said here as Nio It's just like kind of sideless stocked not a whole lot to it there American Airlines alright, this thing's not down a whole lot percentage wise But obviously has a great direction right now much closer to the lows compared to anything that we've looked at so far Airline sector has been getting beat up here. I Always wish there was like a cruise line ETF. I don't think there is but NCLH for right now NCLH dropping off essentially making the same type of move No, just a lot of these you could look to try and rely on as a general market movers You know an auto stock like GM, you know that that stock I've been more interested in lately It's becoming more within my price range of late But you know, this thing has been dropping off pretty nicely across the day today with the market I'm sure you could say same to be said on Ford Ford's a little too slow for my blood though It's like an $11 stock, you know, this is how like Which one was it just before that the cheapie that was a shortable to begin. I think the real stock here This is like real. I'd rather trade real than for just given the pace, right? Basically moving the same all right, so for right now actually that GM stock I like and Maybe I just kind of collectively right air and sea stocks all together just you know group them up as a bunch You know, that's pretty much it folks We ran through across the gainers and losers list if there's anything else that looks great or anything that we've just like missed or Popping right now suddenly by any chance type it in the chapel. Let me know. I mean, I'm all ears You know this is ENDP cheapy moving so I skipped over that at first just because it was a cheapy, but It is pushing back up. I respect it and not only do I respect it I respect it because it's a stock that we are really familiar with here You know as a group Just over the years like just even if you're a new student just so you know over the like many years like five to eight years that I've been here Been here eight years, but like five to eight years that that range like we've been trading ENDP quite frequently off of news or earnings This thing got clobbered over the last year and a half or so But no making a nice squeeze up here So, you know, hey if we've been looking for these short squeezes or dead cat bounces on like, you know, CLVS and You know all these others PEV are EV AERC etc Well, why not look for it here ENDP? So, you know what I like it for right now the endo trip John says oh oh to oh, that's right. You had mentioned that John you I think oh no, no you brought up the Was it uranium one? I think oh to you're saying oh oh to is the direction daily travel ETF all together Gotcha. Okay cool to know You know hey, so if you want to follow any sort of travel or vacation type stocks here You know the more you know here obviously a very spotty chart day trading wise But you know you could just follow this perhaps for like the cruise lines, maybe The more you know RGF on YouTube. I says KZ are so disappointing. I agree. I completely agree But you know what I'm not gonna do though RGF I'm not gonna like keep focused on it across the afternoon I think it's just kind of right in between my levels here that I have from my other chart, so Oh already dropped down to eat. How about that? So, you know this thing is already down to eight now. Wow, all right Well, I'll tell you what this thing dropped off quite a bit after we started the meeting so You know if it already breaks under and over from eight and then looks to make the push Maybe now we do look to put it on our list I thought it was still kind of around like 840 ish like 820 ish kind of lingering around there This thing already shook under and over eight give it space give it time, but if this could build over eight here You know what it's the next whole number down right after nine comes eight You know ten was a big level 12 is a key level 13 was a key level from the after hours yesterday No, hey, you can keep going but let's see it slowly build this support over eight then by three three thirty We see a big spike now actually even more than anything. I'm gonna put this on our watch list I don't know if you folks see what I see but on time and sales. I see a 750,000 share it has to be a dark pool print filled off of 805 filled at the ask I'd say that is a ton of buying slash short covering So at that I would be pretty interested in seeing if this could begin to build over eight to eight oh five and then Run up heading into the close. So you know what I'll give this one more chance. I Took a break from this after I got chopped out around twelve thirty one o'clock But you know what I'll put this on our list here, right? Looks a little bit more interesting now after seeing that, you know Three-quarters of a million share print filled so KZ are one more time Mark says H. E. R. X pop. How about that? So I said I was gonna come back to maybe one or two of these here at the end H. E. R. X You know, hey this ended up making a nasty shape just a moment ago But I appreciate the call out from Mark because it's well timed and you know Trying to make that squeeze. Let's see if this can keep going. I'll put this back on our list This back on the top If it ends up breaking lower than obviously that's a move on but you know nice little continued move here for right now You have a 78,000 share iceberg order on the ask at 280 just two pennies off the high of the day there So there's be mindful of that the high of the day is pretty strong. It seems right off that 280 282 All right folks for right now We're gonna wrap up I'm like eight or seven minutes shy from a coach who called one of our students want to make sure that they get the Lincoln They're good to go but I'll be back on the mic for all of us like Mark Leda yahoo to Carol Jean and Michael and all this just live inside the trading room coming up at 3 30 for all of us in YouTube and Facebook live I appreciate you folks sticking with me each and every day each and every afternoon Any questions that you have I answered back a couple of us actually from yesterday and the day before So if any questions you folks have come in Please let me know you know anything to do with our meetings or call out stack trading or crypto trading education Send it over to Josh at C2 trading comm That's my email address right there again Or if you're if you wanted to join us inside our live trading room feel more than free to do so then just going right down To the link on the yellow banner below right there on the stream just to get yourself started But for all this live live there right now, I look forward to talk to you folks just coming up at 3 30. Take care Come a cyber group member today Just click the link below and receive all these amazing products and a world of knowledge for just $9 do it today


Welcome to the ninth session in the second module on the core signals and systems. You will recall that in the last few sessions we have been extolling the virtues of a sinusoidal input to a linear shift invariant system, particularly a linear shift invariant stable system. Now even after looking at the sinusoidal input, we looked at the two components so to speak of a sinusoidal input, namely the two oppositely rotating complex numbers or phasors. Now all this is very well, if it were fairly general, if it were fairly common that one would have sinusoidal inputs to linear shift invariant systems, otherwise this just seemed like an exercise in a very specific domain of application. What we are now going to develop over the next few sessions is a few ideas which would later convince us that the sinusoidal input is fairly generic. In other words, there is a wide class of inputs which can then be expressed as sinusoidal inputs and therefore one could analyze the response to a large class of inputs by looking at these inputs as a combination of sinusoids. And since the system is linear, one could look at the output to each sinusoid individually and linearly combine the outputs. Now to do that, we need to move to a totally different way of looking at signals and that is what I am going to do in this step. I am going to talk about the relation signals and vectors. So signals which could be either continuous variable signals or continuous independent variable signals or discrete independent variable signals and vectors. If we think about them are essentially combinations of coordinates. So actually it is not too difficult to see that there is a relationship between signals and vectors. You see, let us take a two dimensional vector. Let me draw a two dimensional vector on the plane of this page. So I have this vector. I can decompose the vector into its two perpendicular components, assuming that your so-called axis perpendicular axis are as shown. That means you have unit vectors as shown in green here along these two perpendicular irons. Now, how would you get the component of this vector which I have shown in black? Let me call it V. I have written V here to denote this particular vector. How would I get the components of this vector V along these two dimensions, along these two directions here? I would essentially get it by using what we call a dot product. In fact, let me explain that separately. So how do I take a dot product? Let me expand the view and then explain. If I have this vector which I will call V and if I wish to take the dot product of this vector with another vector u which I am showing here, u may or may not be a unit vector. In other words, we may or may not associate a magnitude of 1 with u. Anyway, the dot products of V and u can be thought of as the magnitude of V multiplied by the magnitude of u multiplied by the cosine of the angle between them. And here, let me denote that angle by theta. And of course, if u is a unit vector, if magnitude of u is 1, then the dot product is simply the magnitude of V multiplied by the cosine of the angle between them cos theta. So essentially you see that what a dot product does is to give you the length of the perpendicular component in the direction of a vector u.  If u is not a unit vector, then you need to divide by the magnitude of u to get that component. In other words, another way to think about it is create a unit vector in the direction in which you want to project V and then take a dot product of V with that unit vector. Now, if I have perpendicular vectors, so as I did in the previous situation, which we showed you, here we had perpendicular vectors. So, if you looked at this one and this one, you could find these two components, the red components here as we showed them, this one and this one individually by taking the dot product with a unit vector in each direction. So, there is a certain decoupling. If you have perpendicular components, there is a certain decoupling of calculation. You can calculate the components individually. On the other hand, you could also have a projection of a vector V along two directions which are not perpendicular. We shall not go into that at this point in time. We need to say that that calculation is not as easy as it is when these two unit vectors are perpendicular. So, right now, let us try and look for situations where we can create such perpendicular vectors. Now, we say this paper on which we are writing is two dimensional because I need only two unit vectors which are perpendicular to one another to completely span the page. That means by taking linear combinations of those two unit vectors, I could create any vector on that page. So, we say a collection of vectors spans a certain space. If all possible linear combinations of that collection give you any possible vector in that space. And if there is only one way in which you can combine those linearly to get the specific vector that you want and this is true for every such vector in that space, what I mean is give me an arbitrary vector V in that space and you claim that there is a collection of vectors u 1 to u n which span the space. Then if it is true that there is only one specific linear combination of u 1 to u n which gives me V, then we also notice that u 1 to u n are in some sense independent linearly independent as we call them. There is no ambiguity about the components. Another way to understand it is there is no way to combine these components u 1 to u n to result in the zero vector. So, that uniqueness of decomposition is possible only if these vectors u 1 to u n are linearly independent and then they are called a basis. And even further, if any two elements picked from that basis are mutually perpendicular, then we say that is an orthogonal basis or a perpendicular basis. Perpendicular is a word used more in high school geometry, a more formal word which we use in functional analysis or in the context of signals and systems or in many courses that form the foundations of electrical engineering is the word orthogonal. So, what we have seen in this discussion is the importance of perpendicular vectors. Now, why are we talking about all this? We are talking about all this because we are going to build a relation between vectors and signals. In fact, let me just give you a hint in this discussion and we will proceed more in detail in the next. What is really a two-dimensional vector? A two-dimensional vector is uniquely described by two components. What is a three-dimensional vector? A three-dimensional vector is uniquely described by three components. So, if you say u 1 to u n form a basis for your space, then n is the dimension of that space. Of course, here we are talking about finite dimensional spaces. Now, let us take a discrete signal first. In a discrete signal, you have points at which you define values. Suppose those points are finite, suppose you have only four points at which you have non-zero values. You can see you can liken that to a four-dimensional vector. So, it is very easy to see that if you have a finite length discrete signal, it is like a vector of finite dimension. Well, think about this. We will come back to this in the next discussion. Thank you.


If you're like me, you'd like to have a significant relationship where you feel valued, appreciated, respected, and quite frankly even indispensable to the person you're with. So if you can relate to that, I want you to stay tuned to see how this can actually happen in today's dating dynamic.  Maybe they grew up with you. Maybe they know your family. Maybe they know your friends. And there was a sense of familiarity that certainly was this is what it was like back 50, 60 hundreds of years ago. Now, today, due to our devices, we have access to a variety of different people and quite frankly, they are strangers in our life. Now, why is this important to recognize?