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?
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?