Translations of Mathematical Monographs 1994; 225 pp; softcover Volume: 134 Reprint/Revision History: third printing with corrections 1998 ISBN10: 0821802364 ISBN13: 9780821802366 List Price: US$85 Member Price: US$68 Order Code: MMONO/134
 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, coordinatefree 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
