Zach Weinersmith4h ago
I've decided it's time to just read straight through a linear algebra textbook. Is Strang still the standard?
Show threadPeter Bloem4h ago

@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.

Linear Algebra Done Right

Show threadZach Weinersmith3h ago
@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."
Show threadLavi3h ago
@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
Show threadZach Weinersmith2h ago
@lavi @pbloem Ha, yeah, that's what I figured. I think the problem is I'm not fluent yet. So figured I'd read Strang whose philosophy is examples first, then definitions. Then circle back to Axler for rigor.
Show threadPeter Bloem

@ZachWeinersmith @lavi

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

https://peterbloem.nl/publications/unraveling-pca

Unraveling principal component analysis | peterbloem.nl

1:19pmWeb
Show threadarclight1h ago
@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.