So, the next topic is linear transforms. So, suppose we have u and v, these are two vector spaces over a field f. Then a mapping from u to v is said to be a linear map if two conditions hold or a transform if 1 f of u1 plus u2 equals f of u1 plus f of u2 for all u1 u2 in this first vector space. And the second is that f of lambda u is equal to lambda f of u for all lambda belonging to this field and u belonging to the set u vector space. So, these are the two conditions that define a linear transform. Often this is written compactly as f of a1 u1 plus a2 u2 is equal to a1 f of u1 plus a2 f of u2 for all a1 a2 in this field f and u1 u2 in this vector space u. But this is just another way of writing it. So, you may or may not agree that this is a more compact way. To me, this is a slightly more intuitive way of writing it. Okay. So, some properties of a linear transform are that the values of f over on some basis of u completely defines f.  So, if you can write it as a linear combination, then if you know what values f takes on the basis, then you can find its value for any other u that belongs to this vector space capital u. Second thing is that 0 always maps to 0. So, one way to see it is if you just substitute lambda equals 0 here, you have lambda times f of u, whatever f of u is, this is 0 and lambda times u is always the 0 vector. And so, one very important property is that any a r to the m by n is a linear transform from r to the n to r to the m and vice versa. And another property is that matrix multiplication, this is something I mentioned in the previous class also, matrix multiplication is the corresponds to a composition of linear transforms. Sir, one doubt, this previous property you told that the linear transform from rn to rm and vice versa, what is meant by that vice versa part means rn to rm? No, I don't understand that. Yeah, so that's a good question. So, any matrix a is a linear transform from rn to rm and vice versa means that any linear transform from rn to rm can be represented as a matrix a. Okay, thank you. Sir, can you explain that part again, the value taken by f on some basis of you completely determines f? Okay. So, suppose this u has a basis u1 through u11 and it's f of un. So, suppose I know these n vectors, then any u in capital U and u equal to alpha 1 u1 plus less alpha n, we've seen that this representation is unique. There's a unique linear combination, which gets you to u when u1 to u1 is a basis for this space capital U.  So, this is what I mean by saying that the values taken by f on the basis completely determines f on all vectors in capital U. Is it clear? Yes, sir, thank you. Sir, is there any relation between basis of u, basis of v and the function? Suppose if u and v are of same dimension. Yeah, so that's what I'm going to talk about now. Vector spaces associated with linear transform. So, you might have heard this rank nullity theorem. Okay, and this is closely related to that. So, I'm going to talk about that now. Okay, before that, maybe I'll make a couple of remarks. So, one thing is that the way I define this linear transform here, it's a transform from u to v. And it satisfies these properties. Now, it's possible that there are some points in v which are not reachable as f of u for any value of u. What I'm trying to say is that the way it's defined here, u and v are two arbitrary vector spaces. And not every small v in this vector space capital V is required to be reachable by taking f of u for some u in capital U. So, that is one point. Another point is that as you can see from here, if u has this basis, u1 through un, and I take v1 through vn, then any u in capital U can be written as a linear combination of these vectors. And so, if I consider only the points that have an inverse map in capital U. So, as I mentioned, not every point in capital V needs to have an inverse map small u. But if I only consider the points in capital V that do have an inverse map small u, that you can show is also a vector space. And now, that vector space, you can see already that any point in that vector space can be written as a linear combination of v1 to vn. But now, it's not clear that, of course, it's clear that u1 through un are linearly independent. There are bases for capital U. But it's not clear that v1 to vn are going to be linearly independent. Moreover, any v which is reachable from this vector space u can always be written as a linear combination of v1 to vn. So, v1 to vn certainly span this set of vectors that are reachable from this set u under this linear map f. But this could be an overcomplete set. In other words, it's possible that there's a subset of these vectors which span that space. But it cannot be more than n. So, the dimension of the space that can be spanned by this u under this linear map f can be at most n if n is the dimension of u. You cannot increase dimension by using a linear map. But it's possible that you end up decreasing dimension. So, does this mean that the v need not be a basis? v1 to vn need not be a basis for the space spanned by u under this transformation f. That's correct. Thank you. So, the first space associated with the linear transform is what is called the range space or the column space. So, now I'm going to refer to these linear transforms as matrices because this particular thing is easier stated using matrices. So, and because any matrix can be viewed as a linear transform and any linear transform can be viewed as a matrix, we can also discuss about matrices. So, range space, which is also known as the column space. So, that's defined as r of a, which is the set of all vectors in r to the m. So, let me say a is in r to the m by n, y is equal to ax, x is in r to the n. It's the span of the columns of it. It is a subset of r to the m. Every vector here belongs to r to the m. In fact, it's a vector space. Now, the dimension of the range space of a is less than or equal to min of m and n. Why is that? Because it is a subspace of r to the m. It's a subset of r to the m. So, it can have dimension at most m and this matrix a has only n columns. And so, if you write y equal to ax with n columns, you can have at most n linearly independent vectors in the span of the columns of it. This dimension of the range space of a is also called what? p. Exactly. Thank you. So, for example, if I have a equal to 1, 2, 3, 5, 4, 3 and 3, 3, 3, then the range space or the column space of a is the set of all linear combinations of any two columns of a. Notice that if I add these two columns and divide by 2, I get the third column. So, these three columns are not linearly independent. So, only two of them are any two of them are linearly independent. So, you can take the first and second, second and third or first and third any two columns and the set of all linear combinations of those two columns is the range space of a and its dimension is 2, which in this case is actually strictly smaller than the min of m and n. m is 2, m is 3 and n is also 3 here. This is a map from r to the 3 to r to the 3. And the dimension for the rank of this matrix a is 2.  So, in other words, it satisfies those two properties we discussed the previous class. Okay, it is Hotel California. You can never leave any two vectors in r of a. If you take their sum, that also belongs to r of a. And if you scale a vector in r of a, that also belongs to r of a. Yes, go ahead. Sir, I have a small confusion. So, given a two pair of vectors with a different dimension, I can always find a matrix a which will transform, let us say, vector b to vector a.  So, you are saying that given v 1 say in r to the n and v 2 in r to the m, you can always find such that v 2 equals a v 1. Yes, sir. Yeah, so that is correct. So, in fact, you can find many such a's. But so what's the point? What is your confusion? So, my confusion is that is transformations always linear in nature? I mean, there is because there are some conclusions. No, what this means is that you can find a linear transform that maps v 1 to v 2. It doesn't mean that you can map v 1 to v 2. And secondly, there can be some non-linear transformation, right? I don't want to look for that right now. It may not be easy to find a non-linear transform, but okay, here is an example. Suppose I had v 1 equal to 1, 2, 3 and v 2 equal to 1, 4, 9. Okay. Now, I can always define a transform f of v equal to I am going to use Matlab's notation here dot power 2. What this is doing is it's taking the square of every element in v. This is a non-linear transform which clearly maps v 1 to v 2. Okay, so it need not be a linear map. But at the same time, we can find matrix A as well to do this transformation, right? Yes. In fact, you can find many such matrices because you only have one constraint. You are giving me one point in R to the n and you are giving one point in R to the m and you are asking me to find a matrix A that will map v 1 to v 2. Of course, this is going to map other vectors to some other points. But in fact, I can find an A that will map if you give me a set of vectors in R to the n and another set of vectors in R to the m. I can ask, is it possible to find an A that will map the first set of vectors one by one to the second set of vectors? Okay. So to answer that question is not immediate from what we've discussed so far. So you should keep that question in your mind and revisit it later. So I'll write it here. You can think about it later.  So this is a very basic question but I don't want to answer it right now. It's something to keep in mind and you can revisit it later. Okay, sir. There are conditions under which this is possible and under some conditions, it's not possible. Okay. Sir, may I ask a question? Yes. Sir, the thing that he told that the elementary square operation that you showed as an example of nonlinear transformation. Yes. So if we want to take any v 1 and get to any v 2, maintaining the relationship that you told that elementary square, so it is not possible to find any unique A, right? Because A is not a nonlinear transformation. Of course, this kind of nonlinear transform, first of all, you cannot express it as multiplying by a matrix A. So this can never be written as A, V for some matrix A. Yes. For general case, we can't find any such A.


Hi everyone, I'm George Kau and I'm excited to be here with Patty Kaye the one and only Patty Kaye Patty, thank you so much for being here Thank you so much for having me. I'm excited about this. Yeah me too So we're gonna be talking about marketing especially for self-employed professionals And let me just go ahead and share Patty's background with you all and then we'll jump into Some very helpful topics about marketing. So Patty Kaye helps self-employed professionals, you know, exact especially coaches consultants and experts get their unique Contribution and genius out of their heads into the world She uses a combination of coaching consulting and word smithing to help people organize their thoughts and articulate their big ideas Her superpower is in taking heaps of rambling info and distilling it into succinct and understandable messaging so this is great Patty and And And you have a you have actually a kind of a Podcast or online class business talk show That's really cool, too And I'll be sure to put that put the link in the notes below But I wanted to ask you about a couple things that you like to discuss with clients one of them is The idea of a target market. We've all heard this idea of what is your target market? You know, that's a very common Phrase and marketing target market targeting people Tell me what you think about that Not much I'm not a fan. I'm not a fan of a lot of marketing language because I find it Dehumanizing so for my clients that coaches consultants experts their relationship businesses Their clients are people and so much of the marketing language that we hear is about target markets It's about leads and prospects. I had a client call them suspects at one point. It's very Dehumanizing other ring. It's not about having a relationship with people or even remembering that these people are People and that your future clients are going to be actual human beings that you have a relationship with and that you like Yeah, yeah, absolutely. It's I love that and it's a good reminder for me, too Because you know, one of the things of course, I do a lot is run Facebook ads and things like that and and in the ad platforms They use the word targeting As as a very common thing they use funnels, too They use all kinds of you know conventional language and it is important to think yes if I'm Talking to real human beings Who have wants and needs? They have you know, and in some cases they're they're hurting. They're suffering. Um, there's things that I can really There's something that I know there's something that I can help them with that can really make a change in their life Like it is such an honor To realize that that is the role that we can play in someone's life is to be a real benefit to them And it's like yeah when we do that then it's marketing takes on a different feel. It's like oh, it's about connecting, right? so the other thing that I The way I kind of rephrase it or invite my clients to look at it differently Is to think about future clients So rather than thinking about your target market or your target audience It's about your future clients, which is a different sort of a mindset Because for one thing It shows that they actually exist like your future Clients are they're inevitable if you're going to have a successful business. You're going to have clients. Those clients are here They're alive. They're they need what you have to offer They want what they want to hear from you. They're going to pay you They're going to hire you because they're your future clients And when you look at that as a you know a distinct group of people that are very similar to your current clients I think it changes how we look at marketing. It's less about how do I find people convince and convert and persuade And it's more about how do I get in touch with these people who are going to who are destined to buy for me I love that. Yes. They are they are they are destined to buy from you because Of the right fit, right? Um, so that actually I want to I want to jump to that that that question that I had for you, which is um You know, you just mentioned convince and persuade so Tell us about that. I mean Most of the time when we learn marketing One of the common, you know topics is persuasion psychology, you know, you're supposed to learn how to find ways to trick their brain into Somehow hypnotizing them right into buying from you. I mean literally um You know, there is a whole branch of marketing called neuro marketing Which is learning how to manipulate other's brains so that they buy from you So, what are your thoughts on that? I hate that I really I really have a problem with it. There's a lot of psychologically manipulative marketing kind of strategies and tactics that are being taught Um, and I think that you know, this fits in with this idea of dehumanizing is that we You know, we lose any kind of care and respect for people When we're trying to get them to do things that they don't want to do and you know Once again coaches and consultants. These are helping professionals and you know, even when you look at coaching And it's like one of these foundational ideas about coaching Is that is that we are all capable and resourceful and we have our own answers And we should have the ability to make good decisions for ourselves and that that's really important And we're taught that in coaching school not to influence people and yet Seems like all bets are off when it comes to the marketing that it's okay Like it's it's it's justifies The means are justified by the end I you know, I had somebody say oh, I'll do anything in the marketing so that I can give that person a transformation and it's like Is that actually really true? Yeah, I'm so glad you're saying this. Yeah, it is it's it's always shocking to me how heart-based You know business owners and professionals they they can they they see the Zagridness of the work they do with clients or the the sort of the yeah the relational aspects the Healing aspects and then like you said when it comes to marketing all bets are off like why why is there such a disconnect? And I think there's a disconnect to me Of course, it's because partly because of fear, right? It's like oh if I don't if I don't do the things that the marketing experts are telling me that I do That's the right way of doing marketing to get clients. I want to I don't want I want to give it the best I've also heard this. I want to give you the best chance, right? I want to give give it the best chance that people will work with me Why would I not do that because I believe in my work once they however they get to me once they get to me Then the healing begins then then the transformation begins then the goodness of my You know spirit and soul it can be there but the marketing Yeah, do do whatever you need to do marketer So how yeah, I love this and and so so so tell me more than If if you're coming to it from a more ethical point of view Now one of the things of course you do is copywriting for people, right? Or helping people with the with the word so first of all What is copywriting? What why why are words important? And then we can get into how we can do this without having to strong arm people and things like that Yeah, well the copy copy writing is your marketing You know, it's marketing words that you use typically, you know your website copy your advertising copy I'll even extend that to Content marketing sharing your expertise that there's an element of copywriting in it In that it is meant to be a marketing piece And you're writing it in order to attract your ideal clients and show them how you can be of service to them So that's that's the copywriting. It's I look at it It's pretty much any place that you use words in your business is kind of a marketing opportunity and copywriting is a way of looking at that as What do you need to Tell your potential clients explain to your potential clients. How do you connect with your potential clients? To let them know that what you have to offer can help them in some way That's my perspective for copywriting. So it's words. Yeah, totally and um, I think some some of us You know, of course, how important the words are and that could bring a level of performance anxiety in there. It's like, okay now I have to be poetic or I have to be really persuasive and like Oh my god, I have I know I only have 10 seconds with them. How do I, you know, make them stay on this page? kind of kind of feel What's your perspective? I mean, you've you've done so much marketing writing for clients and for yourself What's your take on that? Um, I think we put the emphasis on the wrong things. We're wanting to be cute and clever and catchy um creative Completely and totally different from everyone else that we do and the focus is always You know on ourselves. This is what I do. This is how I do it This is why it's different than what other people do. This is how it's better and this is all of the This is what we want to share with people, but what they really want to hear is Are you the right person for me? Can you help me with this problem that I'm struggling with or can you help me get this result that I'm looking for? And they want to be able to clearly and easily understand that And they're not actually interested in any of the differences or the variances or how you do what you do Until you show them that you can help them And the biggest copywriting secret in the world is that your your clients are going to tell you what to say When you're in your sessions with clients when you're doing it, you know, especially in a discovery call in the beginning And you ask them, you know, like what's going on?  What attracted you to this? What, you know, what are you looking for?    It's it's actually really beautiful really helpful Your your your copy can be part of the the goodness that you put into the world Uh, it's really great. I love how simply you put that. Yes. It's like talk to them here why they're Why they're reaching out to someone like you Now let's talk about a situation where okay, well Maybe somebody is just starting out and they haven't had discovery calls yet That's one possibility another possibility is that maybe people have had discovery calls, but they have forgotten What's been said in there? So so, um Well, let's just say that Somebody doesn't have quick and ready access to a discovery call that's being scheduled today or tomorrow or whatever Um, any other tips? How how how can we do this? I don't know. Maybe it's talking to one's friends, but but yeah, any any encouragement there There's a couple of ideas One is you know to kind of use your imagination And this is it's a little bit tricky But to try to look at the situation from the outside in and to look at what you're offering and go Okay, so how can this help people and how will they know that they need this help? What are the symptoms that they're experiencing?  You know, what are they complaining about and what is the actual language that they're going to use like real people language? You know, what are they what are they complaining about? You know, maybe it's a coffee shop Maybe it's a pub and they've had a couple of glasses of wine You know, but what are you know, how are they expressing the problem? Like what makes you want to kind of swoop in from the fly on the wall swoop in and land on the table and say Hey, I can help with that Yeah, that's really really good. Yes and um So this thing what you just you just said about how the marketing copy So many of us go into Our own story like like the homepage or the or wherever whenever we share about our work It's so much about our own story But you just said that well, maybe they don't care so much about that until They know That you can help them and I love that because It's that old saying it's like people don't care what you know until they know that you care, right? We like we've all heard that before and what you're just saying is like, okay, that's true in writing your Website or your social media profile or whatever wherever people are discovering your work is that Can you show that you care? Not just about yourself and your own story, right? Like can you show that you care by by the fact that you understand what they're going through like what what they're needing, right? So tell us more about that like Because it's happened so often. I see it all the time. It's like how can we make that shift more Well, one of the things that we can do is just think like it's all the Key to all of this is put yourself in the client shoes And even just think about this like how you like if you're going to create your website think about how You would buy and what you would look like look for when you go to a website, right? And the first thing like we don't want to waste our time and we're not interested like this is kind of a strategic Kind of a thing It's like you go to a website and the first thing you want to know is am I in the right place Can can this is this the answer that I'm looking for right? And it's kind of like just to use a simple example like let's say You're looking for a mechanic and you have a certain kind of car The first thing you want to know is do you fix the kind of car that I have? And do you fix the kind of car problem that I'm having? I don't need to know about your certifications or how you're better than the mechanic down the street Because until I know that you can fix my car With the problem that my car is having I don't care about that stuff Now once I know that you can you know that you work with my kind of car and you work with the kind of clunk clunk noise that it's making Then I want to know the other stuff now. Now. I want to know. Okay. Who are you? What you know, are you honest? Are you ethical? Am I going to like you? Are you qualified to do the work that you're doing? Like that's when I care But but until I know that you can actually help me solve my problem I'm not interested Yeah, it's like people imagine going to mechanics website and the first thing they say is well, let me tell you When I decided to become mechanic, you know, I had this I went to the mountaintop And I had this experience and God spoke to me and said you need to be a mechanic And that's why today I'm a mechanic. It's like wait, but do you serve as Honda's? Do you work with do you work in this kind of Ford car? I mean Like I'd like to know that you know and and do you work with suspension issues or whatever it is Like that's what I'm dealing with. I think I'm not even sure, you know, can you help me figure it out? Right And that's that's a really good example too. It's right like suspension issues Like do we know that it's a suspension issue or do we know that you know? Like it's really bumpy when we're driving over bumps or something like that or like we know that it goes clunk clunk clunk We know that it doesn't run And it's just then they give all like, you know the laundry list of things that could be going wrong with it It's all mechanical terms and jargon that we don't understand And that you know from a consumer's Perspective that kind of gives that It feels inapproachable. It's like I'm not sure this person actually speaks the language that I speak I'm not sure that they're going to listen to me and understand. Am I going to feel foolish when I go in and start talking about clunk clunk clunk? Um, like, you know, what what if the the site says, hey, is your car making weird noises? Is it's you know, did it stop running? Does it have this kind of problem? Then you can go? Yes. Yes And here's somebody who speaks my language. I can understand them. They can help me Yeah, that's so great and Speaking the language is exactly right. It's like Yeah, it's like if I if I don't read greek and I go to websites greek And but that's how so many of us do it. We use very Transformational and flowery language because it sounds good to us. It sounds poetic to us But no client has ever said those things to us Right. No client actually uses though that but yeah, so thank you so much for saying that So I'd love to just kind of hear more about the way that you do your work with clients And those who are watching I'm sure some of you are are interested in kind of working maybe working more with patty. So So I know, you know, yeah, just kind of start from a client comes to you What do you typically help them with and how do you how do you help them with that? Yeah, uh, well the clients I specialize in are the ones that have a really hard time explaining what they do Okay, they they are When faced with a lot of people I know It's a lot of people who do coaching and consulting work because it's hard to explain You know, it's not you know, it's not as easy. Bookkeeping is easy to explain. Everyone knows what it is Mechanic even is easy to explain A mechanic is easy to explain.  But when you talk about coaching and consulting It's more difficult to sell and I think that this isn't acknowledged enough In marketing circles is that it is harder to sell than bookkeeping So it's hard to encapsulate what you do, especially if you do multiple things If you're in If your offer service that people are not familiar with or that practitioners do in a different way Coaching is not a one-size-fit-all term every coach coaches differently They work with different clients. They they work on different areas of their life. They have a different approach Like it's all different. Um, so immediately that's more difficult to explain People don't necessarily know that they need a coach or a consultant. They just know that they have a problem going on So it it is difficult to explain So you can't my clients can't put their their description into a 30 second networking introduction or they can't come up with the home The headline for their home page to you know, succinctly summarize what they do They find themselves kind of rambling on when they're talking to people not being able to fully express themselves They have situations where they know they can help somebody but they just can't get The information across in a way that makes sense to them Um, and and you know stock trying to figure out how to write write their write their copy or their or their content Like those are my favorite clients to work with Yeah, that's that's why I specialize it. That is so that is such helpful work. Um Yeah, so it's so helpful to hear. I mean, of course and not surprisingly you're good at describing What it is that you do and so all right, so now that this person and oh also I maybe uh related or maybe not related you could tell me if this is too much to get into but What about somebody who says well? um I I I I have several different things that I do I love you know Really? Yes, tell us more. Yeah my my process by the way is to I'm not really sure exactly how I do it, but I when I work with a client I ask a lot of questions. I listen like I'm not talking about, you know, fill in my questionnaire and we'll have a You know a 45 minute consultation. I often take hours with my clients letting them tell me everything Everything about what they've done. I ask questions about their clients and about the kind of you know For them to give me examples of their work. I will read all of the stuff that they send me I've read, you know, here's here's, you know 20,000 words that I've written And I just I just take it all in I take it all in take it all in And then like I can't help somebody write their messaging unless I get what they do So I take the time to get it and it's it's totally okay Ramblin tell me everything if we need to make another appointment so you can tell me more. Let's do that Um, so I take in all the information. I understand it and then I'm like, okay in summary This is what I've this is what I've pulled out. Does this look like like you have we missed anything? And then we've got something to work with and we we kind of flesh it out. Um, but That is the thing that I do. I I don't really know how I do it, but it is what I do and That's how we that's how we arise arrive at the words But mainly what I'm doing is I'm filtering for how does this help the client? I'll just help the client. How does this help your client? Right, you know, this is a result or a problem. I'm always filtering for that stuff Um, the rest of the stuff is great. And I mean it can go into content marketing. Some of it can go into your Out page. Sure. Really the succinct pieces that sell your services are about what you do for your clients Yeah, wow and I bet the kind of listening you do I mean You know, I can tell that you really care about your clients. I mean your your process demonstrates that And um, wow, what what what a difference. Thank you for for sharing that. So, okay, let's say that you now have Done the intake you've gotten their their story They're all the things that they love doing with with with people they want to you know, how they serve people So now what do you do now now you you send them a summary and now now what happens? Yeah, I send them a summary often with a with a diagram of visual because sometimes When you're talking about complex or complicated or you have a process it needs a visual It needs a Venn diagram or needs a process error or some kind of you know Some kind of a visual to help explain it Which is really helpful for for when you're talking to clients About what you do is you can you know grab a piece of paper and Draw it out and explain how a process works. So it So there's a visual and then there's some notes and at that point People can write their copy of themselves because I give them all the high points. Basically, it's like here's an overview of what you do Here's the one sentence summary Here's you know, here's You know the outcomes that your clients are looking for here's some notes about the ideal client profile and they end up Two pages may be diagram and some notes and that's you know, this is kind of This is the guide for everything that you ever want to write It's always going to come back to this because we've you spit it all out and here it is It's always going to come back to this and then if they want help with their you know Actually writing the content the copy and content. I do that collaboratively. I don't do it for them I do it with them because it needs to sound like you like if it's going to be authentic It needs to be your words and needs to sound like you. So I work collaboratively Collaboratively kind of copying content coaching to help people I'm so glad I'm so glad you said that because I Have worked with so many copywriters over the years Sometimes for my own stuff, but sometimes as clients or sometimes as the business partners They have copywriters that I'm interfacing with and I'll tell you it's like I just never Yeah, it has to be in your own voice. You can't have someone write your copy Like I mean you can of course people do it all the time But it's like so obvious to me This email was from you this email was from your copywriter. I can tell It's like it's like it's a two different emails. It's like two different voices two different people writing it It's like no matter how close Yeah, so I'm so glad to hear that you do a collaborative with people rather than just like well Let me just outsource it all to you. So thank you for doing that I mean first you you help them create the messaging That becomes clear as a template But then they do the writing and then you help them with that too. That's that's amazing. That's really helpful awesome, um, so Let's as we complete tell us about that the the kind of the the free classes that you do Slash business talk show tells about that Yes, I work I work with a with a partner george and she is a she's um We jokingly say that I'm boxes and arrows and she's hearts and flowers So my thing is more of a strategic Can the words and hers is helping people figure out exactly what it is that they want Figuring out what their purpose in life is their values helping them break through blocks and Fears that keep them from moving forward and helping them create really good relationships with people So our so we come together. We do this talk show our thing is the u-shaped business and we talk about Self-employed entrepreneurship figuring out what you want doing good work in the world Having a business that's based around your purpose and on your values working with the people that you're here to serve How to connect with them how to talk to them overcome your your stuff and also my stuff the strategy and the words and every wednesday at 9 30 we teach Uh, we we teach something and we talk about a subject and we basically just share everything that we know We we share it all our our You know my perspective is that when you do work with clients Implementation kind of work helping them do stuff. You can be really free with the information That's not what they're looking for. They're looking for the support. So yeah freely give information. That's amazing and Just be clear that these classes that you do people can join on zoom live, right? And it's uh, it's That's really cool. That's really cool. Well patty. I will be sure to put the link below So folks go check out patty's, you know live zoom classes that are free Very generous and of course the work that she does it now you've now you've heard how she does it And that that's something that you can get some help with please, you know, reach out to patty So thank you patty so much and also I just want to also thank you for being such a supporter of my business and things like that It's been it's been so i'm so grateful for your support as well so Anything else you want to say any words of encouragement as we complete? um The work that you do in the world matters And it's important when you're called to be a service in this kind of way. It's it's it's a beautiful thing and uh, yeah Thank you so much. Thanks patty. All right, and uh, you'll find uh, the links below folks and go check out patty k's work Thanks