Zach WeinersmithI've decided it's time to just read straight through a linear algebra textbook. Is Strang still the standard?
Andrew Shields@ZachWeinersmith I don’t know, but if I may be allowed to be nepostic, I learned linear algebra from the 1980 edition of my father’s textbook, and I thought it was excellent: Elementary Linear Algebra, by Paul C. Shields. Of course, I had the advantage of being able to consult with the author. 😉
Peter Bloem@ZachWeinersmith If you want to read one cover to cover I can recommend https://linear.axler.net/
It also depends a bit on what you want to get out of it. Axler is good to get the more abstract perspective on linear algebra.
If you just want a concrete understanding of what an SVD does to a grid of numbers, it's probably not the best one.
@pbloem I tried Axler but he's SO abstract I get tripped up. I keep reading sentences that feel like "1+1 equals two, which you should verify."
Lavi@ZachWeinersmith @pbloem I loved this treatment but it’s definitely written specifically for math folks. I will say it could be worth trying again, maybe even after reading something else because it provides lots of real math insight and understanding the how/why that is often dropped in favor just teaching the algorithms in some other textbooks
I think standard textbooks like Strang focus too much on row reduction as a building block and too little on the idea of a matrix as a transformation of space (which is the most intuitive starting point for me).
I don't know of any textbook that does that but (if you'll forgive the plug) I wrote a long-from exploration of PCA that takes that perspective and touches on most aspects of concrete linear algebra
arclight@pbloem @ZachWeinersmith @lavi I had some success with Strang recently but would really like something that goes in a more intuitive direction like transformations of space. At some point it all becomes blah-blah-blah-symbol-manipulation which isn't very helpful.
@ZachWeinersmith @pbloem this is very reasonable. And likely you’d find Adler more insightful after having a grasp of examples and general definitions
Vini Vendramini@ZachWeinersmith that’s what I used 10 years ago. Not sure if there are any better textbooks per se, but there might be helpful stuff on the internet (like tutorials with interactive graphics and stuff) to complement your reading.
for the sake of it, or to do something in particular, I find learning is generally more fruitful when it's in the purpose of something, and you need to learn it *because of* something
@ZachWeinersmith
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@p The because-of is a book project :D
mpark@ZachWeinersmith When I was in school, I found Strang's lectures at MIT on the subject to be incredibly useful. If you're open to a non-book option, that is.
a wandering happenstance@mpark @ZachWeinersmith Yeah, Strang is still great, and Strang’s lectures are a great supplement.
Trebach@ZachWeinersmith We used Linear Algebra by Jim Hefferon in Math 310 at VCU. He put it online for free: https://hefferon.net/linearalgebra/
the roamerI'm not up to date on recent Linear Algebra textbooks, but hey! Strang's book is uniquely beautiful, and uniquely effective in conveying deep structural insights elegantly and with concrete examples that stay with the reader. Perfect for a class setting, but also eminently suitable for self study. The right choice for your project! (imho)
Each field has a textbook that is accessible to inexperienced readers yet true to the deeper structures of the subject. That book ought to be written in every field, but in most fields it never is written. It requires a gifted author to come along and do the deed. Gilbert Strang's writing of his book was one of these special and rare events.
As it happens, linear algebra had another such event, a generation before Strang, in the shape of Paul Halmos's Finite-Dimensional Vector Spaces. Another beauty, on the abstract side of the spectrum, and perhaps the perfect complement to Strang.
Joseph Giubardo@ZachWeinersmith my alma mater uses Lay for the intro/engineering course and Axler for the senior level course.
Brian McCallister@ZachWeinersmith I did better with Savov’s No Bullshit Guide, but I think Strang is still the canon answer.