Matrices and Linear Transformations: Second Edition

Matrices and Linear Transformations goes right to the point. The text is clear and concise and is illustrated by a limited number but very helpful set of examples. The proof are easy to follow but are rigorous. This is without a doubt my favorite book about matrices.

This book is concise and possesses a great deal of information on matrices. I had to buy $100+ book for a upper division linear algebra class and it sucked; it contained in 300 very cluttered and long winded pages what this book accomplishes in a little over a hundred pages with far greater depth. It's a highly affordable book and quite well written, which, I guess, is why they don't use this book to teach linear algebra in a 'modern' classroom.

So many math books take a relatively simple topic and with the use of horrible notation and confused english, convert it to something esoteric and complicated. This book, however, is anything but that. It involves mathematical rigor, covers a broad range of topics and has answers to selected problems at the back which for a math book, works real well for me. Besides you can't argue with the price.This book never leaves my desk, recommended strongly.

Charles Cullen deserves to pat himself on the back for this one. The first three chapters are the meat of the book which review or, possibly to some, introduce the fundamentals of linear algebra (matrices, vector spaces, and determinants.) After firmly laying down a foundation from which to work with, Cullen does a remarkable job explaining linear transformations and eigenvalues and eigenvectors (although, some basic calculus is assumed known). After introducing matrix similarity and Jordan-canonical form, Cullen dabbles in polynomial matrices and more similarity with divisor theorems and polynomial matrix canonical form. Finally, rounding third plate are an intro into formal matrix analysis (in which some upper-level, although not necessarily advanced, calculus is necessary) and numerical methods. Although these two chapters only encompass about 35 pages total, they do offer a solid foundation for further study. I recommend this book as it breaks a lot of steps involving matrix calculations down and allows the reader to not only understand how, but why.