Textbook in PDF format

This book helps students to master the material of a standard US undergraduate first course in Linear Algebra. The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is the book’s audience: sophomores or juniors, usually with a background of at least one semester of calculus. The material is accessible, coherent, and elegant. And, examples are plentiful. Helping readers with their transition requires taking the mathematics seriously. All of the results here are proved. On the other hand, we cannot assume that students have already arrived and so in contrast with more advanced texts this book is filled with illustrations of the theory, often quite detailed illustrations. A student progresses most in mathematics by doing exercises. The problem sets start with routine checks and range up to reasonably involved proofs. I have aimed to typically put two dozen in each set, thereby giving a selection. In particular there is a good number of the medium-difficult problems that stretch a learner, but not too far. At the high end, there are a few that are puzzles taken from various journals, competitions, or problems collections, which are marked with a ‘?’ (as part of the fun I have worked to keep the original wording)