Linear Algebra

Below is a list of reviews of books on linear algebra.

Linear Algebra
Friedberg, S. Insel, A., Spence, L. (4th Ed. 2002). ISBN 9788120326064.
No prerequisites, but being able to write basic proofs will help in the beginning.

This book is a solid introduction to linear algebra, and starts with the vector spaces and linear transformations, then motivates matrices, and proceeds onto other fundamental ideas like determinants, characteristic polynomials, diagonalization, inner product spaces, and canonical forms in a sensible order. This book is great for first passes through linear algebra, and only suffers from the lackluster chapter (chapter 3) about the computational aspects of matrices.

The Matrix Cookbook
Petersen, K. B., Pedersen, M. S. (2012). Free Download.
Linear algebra required

The Matrix Cookbook is not quite a textbook. Instead, it’s a collection of matrix identities covering all sorts of topics. It is an exceptionally useful reference, especially if you’re doing anything with matrices. Ever wondered about the derivative of the logarithm of the determinant of a matrix? It’s got you covered.

Linear Algebra
Hoffman, K., Kunze, R. (2nd Ed. 1971). Free Download.
Knowledge of basic set theory and decent proof writing and abstract thinking ability

Hoffman & Kunze is a solid 2nd (arguably 1st for math majors) exposure to linear algebra - it is elegant, enjoyable, and concise, but leaves nothing skimmed over. It will show you linear algebra in painful detail, and unlike other books, this book’s pedagogical approach is unconventional as he presents specific examples leading to theorems and definitions with great motivation. There is a wide variety of exercises after each section ranging from routine applications to extremely challenging ones. This book (as mentioned by the authors) has no concessions for non-math students and won’t teach you a hodgepodge of techniques but will provide an understanding of basic mathematical concepts. The book is self contained and a great reference for linear algebra.