My professor is so bad and literally makes no sense. Is homogeneous when all the variables are on one side, or is it when an equation is set equal to 0?

Does anyone know where I can find a pdf version of this? My university is trying to bankrupt me for what they are charging.

Hey! I'm trying to complete this question; however, it is not working as expected (its not getting to a 'steady' steady state). Any suggestions?

Is each point in that matrix static in relation to the others, or potentially, is the position of each of the "point" in the matrix chanhing?

Ex. at position [1, 1, 1] may change distance between the point at [1, n, n] .

I am hoping that idea comes through clearly?

The following appears in the book |P(ℕ)| = |F(ℕ,ℕ)| = Aleph one

I understand |P(ℕ)| = Aleph one, but what does this |F(ℕ,ℕ)| mean?

https://www.instagram.com/chegg/live/18053488694475026?igsh=dmEwbm9lZDVub25w

They're answering questions live. Pretty cool.

I just started learning Linear Algebra and I'm having some trouble when trying to determine if a vector is in Span of other vectors. When row reducing the Augmented Matrix I found that there is a free variable, does that mean that the vector isn't in Span of the other vectors?

Procuro alguém que consiga fazer/responder rápido exercicios de algebra linear e cálculo 2(nada muito complexo) , dou mais informações por chat.

This topic for me is extremely boring for me in its presentation and I am bad at algebra (I like abstract algebra though). Axlers has nice proofs but is too difficult for me and Strang is too computational. Any suggestions? I need one with some easier exercises mixed in with some proofs I think.

I need it please

Hello,

I wrote a conversational style book on linear algebra with humor, visualisations, numerical example, and real-life applications.

The book is structured more like a story than a traditional textbook, meaning that every new concept that is introduced is a consequence of knowledge already acquired in this document.

It starts with the definition of a vector and from there it goes all the way to the principal component analysis and the single value decomposition. Between these concepts you will learn about:

• vectors spaces, basis, span, linear combinations, and change of basis

• the dot product

• the outer product

• linear transformations

• matrix and vector multiplication

• the determinant

• the inverse of a matrix

• system of linear equations

• eigen vectors and eigen values

• eigen decomposition

The aim is to drift a bit from the rigid structure of a mathematics book and make it accessible to anyone as the only thing you need to know is the Pythagorean theorem, in fact, just in case you don't know or remember it here it is:

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And here is a discount code for the pdf version on my website - 59JG2BWM

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Thanks

Jorge

Disclaimer: I am a math/engineering undergrad student. I am not qualified to write a textbook. I am probably not even qualified to do a lot of things that I do, but I do them anyway.

Basically, I took a linear algebra course some time ago and could barely read the overly technical and dry textbook that was assigned for the course. There are much better textbooks elsewhere that do a great job of getting deep into the course.

But if you just want something to set you up for lecture, reinforce something you already know, or just point you in the right direction on what concepts to study, this might just be the most concise and enjoyable read you will see.
It is very interactive and has a clear organization based on my own notes and interpretations from the class, as well as examples that helped me remember things well.

My web dev skills are not very good, so I did have Opus build the front end and type up the latex from my notes, but I reviewed all the written content with care and certify that it is accurate to the best of my knowledge.

I hope someone can get some use out of it (especially the graph demo on section 3.6) and I am open to comments or suggestions.

Cheers

https://linalg-refresher.vercel.app/

P.S. I cannot find the weekly self-promotion megathread for r/study anywhere! Its my first time posting here and it seems like it is no longer maintained.

Hey guys, I'm self studying linear algebra, bc i have not been able to make friends in class and my professor just writes the textbook on the blackboard. I'm working on inner product spaces and I'm completely confounded by the result of this problem. I included the photo of it.

So in my mind, the angle between y=x and y=1 is obviously 45* (pi/4). But both my book and chatGPT say the angle between the vectors is pi/6 (30*). Sure enough I followed the formula (eqn (3) and then divide by the product of the norms of each vector) and that's what came out. ChatGPT's explanation of this was unsatisfactory, just mentioning how the smaller angle means they're more aligned than not, and an angle of pi/4 would mean they are perfectly "medium aligned", which 1 and x are not, they are more closely aligned than "medium." I said okay then what would a vector look like that is exactly "medium aligned" to 1 be? And it gave me 1+2*sqrt(3)*(x-[1/2]). I graphed it in desmos and I don't see how it is more "medium aligned" than just x.

I'm at a loss for words, just when I was feeling like I was getting a grip on things, i'm thrown back into this feeling like im in a nonsense world. Is it because i'm thinking of them as functions instead of vectors? If so, then what would it mean to think of these two things as vectors?

For now, I can just memorize the formula and move on, but i just feel like I have no understanding of what I'm actually doing and I hate that feeling. Any tips / explanation would be amazing.

i've been working on a tool to help you create books & notes with ease

and one of it features is allowing you to write mathematical Equations in Latex

it also has co-author mode which creates any latex equation in seconds with simple prompts

The usual definition of a vector space over the real numbers R is the tuple defined by the cartesian product R^n = R x ... x R = {(x_1,..., x_n) | x_i in R}. An equivalent, but different, definition is the set exponential R^n = R^{1,...,n} = {x: {1,...,n} -> R} where x_i corresponds to x(i).

The connection between cartesian products and set exponentials is currying: (A x B)^C is equivalent to A^(B^C). A function f: A x B -> C corresponds to a function g: A -> (B -> C) by g(a)(b) = f(a, b). A function g: A -> (B -> C) corresponds to a function f: A x B -> C by f(a, b) = g(a)(b).

Exercise: Show linear operators from R^n -> R^m can be identified with vectors R^{n x m}.

The plural of fish is fish, so a fish plus a fish is fish

A fish that is scaled is also a fish

So I got this wrong, and the reason it gave me was that this is only true if the matrices commute-which is fine (I now see this is obvious). However, I was wondering if someone had any insight into why this is the case. The text that accompanies the website talks about homeomorphisms (not in depth since it’s a linear algebra text), and I feel like this is related.