Linear Algebra

by Richard Kaye, Robert Wilson

Linear Algebra provides a valuable introduction to the basic theory of matrices and vector spaces. The book covers: matrices, vector spaces, bases, and dimension; inner products, bilinear and sesquilinear forms over vector spaces; linear transformations, eigenvalues and eigenvectors, diagonalization, and Jordan normal form; and fields and polynomials over fields. Abstract methods are illustrated with concrete examples, and more detailed examples highlight applications of linear algebra to analysis, geometry, differential equations, relativity and quantum mechanics. Rigorous without being unnecessarily abstract, this useful and concise guide to the subject will be important reading for all students in mathematics and related fields.

Genres: Mathematics

242 pages, Paperback

First published April 9, 1998

Reviews

[Hobart Mariner · Rating 4 out of 5]

Nice short second course in linear algebra, favoring a traditional approach to stuff like bilinear forms, Sylvester's law of inertia, eigenvalue decompositions, and the Jordan form. Tries to strike a balance between proofs, worked examples, and "applications." Sometimes the proofs skate over details which would be tedious to pin down, but some of the proofs could have been more rigorous. (I was a little annoyed that it didn't treat base cases in several inductive cases.) There's not too much abstract/general stuff -- the authors mention stuff like changing the base field, and there is some optional reference to finite fields, but mostly the book treats the stuff over real/complex numbers. They do a good job filling in the details for both the real and the complex cases.

The worked examples are very useful references for people first learning this stuff, particularly somewhat less common stuff like Jordan form. It would have been nice to include rational canonical form and Smith normal form as well, especially working out examples for both. Some people might fault the book for only including a few exercises at the end of each chapter, but I think it makes it a quicker read.

Good easy reference for people working in stats or other applied subjects who had a weak first course, as well as prep for grad students who need to fill in the gaps. Could be particularly useful to read right before studying the structure theorem for f.g. modules over a PID. (This book *doesn't* cover the structure theorem but having gone through the Jordan form beforehand does wonders to motivate the more general result.)

[srinivas C]

Haven't actually gone through this book, but have gone through some of the course notes of the same professor (R A Wilson) and they are excellent. So I think this book would be a more carefu and through exposition of topics by the same prof.