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A prominent sentiment in the comments here is that this resource isn't that good. I only studied up to Calculus II, so what would be a good resource to approach

A prominent sentiment in the comments here is that this resource isn't that good. I only studied up to Calculus II, so what would be a good resource to approach LA?

peterhalburt33 5y ago
It really depends on what you’d like to learn LA for, and how comfortable you are with abstraction: LA can span from concrete multiplication of matrices and vectors all the way to very abstract (e.g. vector spaces over general fields or even modules over rings). I know many people recommend Gilbert Strang’s introductory linear algebra (I have not read it, but it seems to fall into the former camp), but I might also recommend Sheldon Axlers Linear Algebra Done Right. In all honesty, I learned La the best from David Griffiths quantum mechanics text, although it is not a comprehensive in its coverage of the subject (not that it should be, given that it is a physics text). I guess I am trying to say that there are many different flavors and interpretations of linear algebra, and while matrices and vectors may be simple at first, it does tend to rob the subject of its richness and depth (e.g. what do these matrices represent, what are the canonical structures etc.) so I am a bit biased towards going full generality at first, and perhaps reading a more rote computation book on the side (I understand we all have limited time though).
- wrycoder 5y ago
  Strang’s latest book is very much in the abstract camp, but very practical. A physicist’s linear algebra book. https://math.mit.edu/~gs/everyone/ https://math.mit.edu/~gs/everyone/
vecter 5y ago
3b1b’s Essence of Linear Algebra videos on YouTube do the best job I’ve ever seen of explaining the intuition and motivation for linear algebra and matrices. They aren’t a complete course in and of themselves. For that you’d need a textbook. But having learned LA the traditional textbook way and then watching the 3b1b videos a decade later, I would strongly encourage you to watch his videos first before opening a textbook. Once you understand the intuition, the stuff you read in textbooks makes a lot more sense and are much better motivated. Math is about concepts, structures, and relationships. It’s not about definitions and theorems. We use those only to formalize the concepts that we’ve thought of. That’s why I recommend the “intuitionist” approach for learning math. You can fill the computations and proofs later.
- laplacesdemon48 5y ago
  Here's another vote for 3Blue1Brown's series on linear algebra [1]. Spending a few hours on this series will easily save you dozens of hours when going through a comprehensive LA textbook. [1] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...
sealeck 5y ago
Linear Algebra by Shilov is worth a shout, and as will all Dover maths books remarkably reasonably priced.
pastaguy1 5y ago
Sib comments are suggesting textbooks (good ones at least, IMO), but FWIW, if I were trying to give someone a 1 or 2 hour intro to LA, it would be: - Strang's 4 subspaces: https://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf https://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf , and just enough supporting material to understand that at a basic level, and hopefully finishing up with the SVD, which to me is basically a summary of LA in one equation. - A quick look at the eigenvalue problem, Ax = 𝛌x, with the key note that hey, in the vast majority of cases, Ax does not equal a scaled version of x (it took me way too long to realize that's what we were doing here when I was first learning LA). <roll tacoma narrows bridge tape here>

A prominent sentiment in the comments here is that this resource isn't that good. I only studied up to Calculus II, so what would be a good resource to approach LA?

peterhalburt33 5y ago

It really depends on what you’d like to learn LA for, and how comfortable you are with abstraction: LA can span from concrete multiplication of matrices and vectors all the way to very abstract (e.g. vector spaces over general fields or even modules over rings). I know many people recommend Gilbert Strang’s introductory linear algebra (I have not read it, but it seems to fall into the former camp), but I might also recommend Sheldon Axlers Linear Algebra Done Right. In all honesty, I learned La the best from David Griffiths quantum mechanics text, although it is not a comprehensive in its coverage of the subject (not that it should be, given that it is a physics text). I guess I am trying to say that there are many different flavors and interpretations of linear algebra, and while matrices and vectors may be simple at first, it does tend to rob the subject of its richness and depth (e.g. what do these matrices represent, what are the canonical structures etc.) so I am a bit biased towards going full generality at first, and perhaps reading a more rote computation book on the side (I understand we all have limited time though).

wrycoder 5y ago
Strang’s latest book is very much in the abstract camp, but very practical. A physicist’s linear algebra book. https://math.mit.edu/~gs/everyone/ https://math.mit.edu/~gs/everyone/

vecter 5y ago

3b1b’s Essence of Linear Algebra videos on YouTube do the best job I’ve ever seen of explaining the intuition and motivation for linear algebra and matrices. They aren’t a complete course in and of themselves. For that you’d need a textbook. But having learned LA the traditional textbook way and then watching the 3b1b videos a decade later, I would strongly encourage you to watch his videos first before opening a textbook. Once you understand the intuition, the stuff you read in textbooks makes a lot more sense and are much better motivated. Math is about concepts, structures, and relationships. It’s not about definitions and theorems. We use those only to formalize the concepts that we’ve thought of. That’s why I recommend the “intuitionist” approach for learning math. You can fill the computations and proofs later.

laplacesdemon48 5y ago
Here's another vote for 3Blue1Brown's series on linear algebra [1]. Spending a few hours on this series will easily save you dozens of hours when going through a comprehensive LA textbook. [1] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...

sealeck 5y ago

Linear Algebra by Shilov is worth a shout, and as will all Dover maths books remarkably reasonably priced.

pastaguy1 5y ago

Sib comments are suggesting textbooks (good ones at least, IMO), but FWIW, if I were trying to give someone a 1 or 2 hour intro to LA, it would be: - Strang's 4 subspaces: https://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf https://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf , and just enough supporting material to understand that at a basic level, and hopefully finishing up with the SVD, which to me is basically a summary of LA in one equation. - A quick look at the eigenvalue problem, Ax = 𝛌x, with the key note that hey, in the vast majority of cases, Ax does not equal a scaled version of x (it took me way too long to realize that's what we were doing here when I was first learning LA). <roll tacoma narrows bridge tape here>