3000 Solved Problems in Linear Algebra by Seymour Lipschutz is not a beautiful book. It is not a narrative book. It is a —a rugged, no-nonsense tool designed for one purpose: to build your problem-solving muscles until they ache.
Lipschutz masterfully weaves the "why" into the "how." Every solved problem includes brief theoretical justifications in the margin or within the solution. You never feel like you are just cranking an algebra handle; you constantly see the connection to the underlying theorems (e.g., "By the rank-nullity theorem, we know dim(ker(T)) = ..."). 3000 Solved Problems In Linear Algebra By Seymour
It won’t teach you the philosophy of vector spaces. But it will teach you how to involving matrices, determinants, eigenvalues, and basis transformations. And in the end, that’s exactly what most of us need. Lipschutz masterfully weaves the "why" into the "how