Problems and Theorems in Linear Algebra: Determinants. 1. Basic properties of determinants. 2. Minors and cofactors. 3. The Schur complement. 4. Symmetric functions, sums [actual symbol not reproducible] and Bernoulli numbers

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. There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs 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, the author 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 can serve as a supplementary text for an undergraduate or graduate algebra course. Determinants -- Linear Spaces -- Canonical Forms Of Matrices And Linear Operators -- Matrices Of Special Form -- Multilinear Algebra -- Matrix Inequalities -- Matrices In Algebra And Calculus. V.v. Prasolov ; [translated By D.a. Leites From An Original Russian Manuscript ; Translation Edited By Simeon Ivanov] Includes Bibliographical References And Index. Presents the basics of linear algebra, with an emphasis on nonstandard and interesting proofs. This book features about 230 problems with solutions. It is suitable as a supplementary text for an undergraduate or graduate algebra course.