3blue1brown has a series on the essence of linear algebra as well. It’s pretty great, and could do well as the Why.
I also like Linear Algebra Done Right a lot, but it doesn’t fit neatly into this framework. It’s a bit too rigorous to be Why, not practical enough to be How, and it’s approach differs enough from other books to make it difficult to look things up in.
Linear Algebra Done Right wins the prize for books which deliver on their title, as promised imho. The typical approach with determinants front and centre is a pedagogical dead end. I find Axler’s approach tracked more closely to the uses of linear algebra, rather than historic proof techniques. I’d say it covers the how and why sections—although perhaps the ‘how’ book is the Matrix Cookbook ;). The what will probably have to come from some other discipline: are you working on stats, or differential equations, or something else?
3blue1brown has a series on the essence of linear algebra as well. It’s pretty great, and could do well as the Why.
I also like Linear Algebra Done Right a lot, but it doesn’t fit neatly into this framework. It’s a bit too rigorous to be Why, not practical enough to be How, and it’s approach differs enough from other books to make it difficult to look things up in.
Linear Algebra Done Right wins the prize for books which deliver on their title, as promised imho. The typical approach with determinants front and centre is a pedagogical dead end. I find Axler’s approach tracked more closely to the uses of linear algebra, rather than historic proof techniques. I’d say it covers the how and why sections—although perhaps the ‘how’ book is the Matrix Cookbook ;). The what will probably have to come from some other discipline: are you working on stats, or differential equations, or something else?