There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to know in the best possible form and that any new book would just repeat material in the old ones. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, Prasolov provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It would be a fine supplementary text for an undergraduate or graduate algebra course.

Readership

Undergraduates, graduates and researchers in mathematics and physics.

Reviews

"The exposition contains quite a few refreshing applications ... It is amazing that a book which covers all this incredibly rich material is only 221 pages long. One of the reasons why this is possible is that the best proofs are carefully selected from the existing literature. The proofs are short, complete, and precise. Whenever possible, the author uses an invariant, coordinate-free approach. This is a very nice book."

-- Mathematical Reviews

Table of Contents

• Main notations and conventions
• Determinants
• Linear spaces
• Canonical forms of matrices and linear operators
• Matrices of special form
• Multilinear algebra
• Matrix inequalities
• Matrices in algebra and calculus
• Appendix
• Bibliography
• Subject index