Lectures on Linear Algebra

by Donald S. Passman

This book consists of the expanded notes from an upper level linear algebra course given some years ago by the author. Each section, or lecture, covers about a week's worth of material and includes a full set of exercises of interest. It should feel like a very readable series of lectures. The notes cover all the basics of linear algebra but from a mature point of view. The author starts by briefly discussing fields and uses those axioms to define and explain vector spaces. Then he carefully explores the relationship between linear transformations and matrices. Determinants are introduced as volume functions and as a way to determine whether vectors are linearly independent. Also included is a full chapter on bilinear forms and a brief chapter on infinite dimensional spaces.The book is very well written, with numerous examples and exercises. It includes proofs and techniques that the author has developed over the years to make the material easier to understand and to compute.
Vector SpacesLinear TransformationsDeterminantsBilinear FormsInfinite Dimensional Spaces
Upper level undergraduate math majors and graduate students.

252 pages, Kindle Edition

Published March 16, 2022

About the author

Donald S. Passman is the author of All You Need To Know About the Music Business and a graduate of the University of Texas and Harvard Law School. He practices law with the Los Angeles firm of Gang, Tyre, Ramer, Brown & Passman and has specialized in the music business for more than forty years.