Softcover ISBN:  9780821802366 
Product Code:  MMONO/134 
225 pp 
List Price:  $90.00 
MAA Member Price:  $81.00 
AMS Member Price:  $72.00 
Electronic ISBN:  9781470445423 
Product Code:  MMONO/134.E 
225 pp 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 

Book DetailsTranslations of Mathematical MonographsVolume: 134; 1994MSC: Primary 15;
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.
ReadershipUndergraduates, graduates and researchers in mathematics and physics.

Table of Contents

Chapters

Chapter I. Determinants

Chapter II. Linear spaces

Chapter III. Canonical forms of matrices and linear operators

Chapter IV. Matrices of special form

Chapter V. Multilinear algebra

Chapter VI. Matrix inequalities

Chapter VII. Matrices in algebra and calculus


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


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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.
Undergraduates, graduates and researchers in mathematics and physics.

Chapters

Chapter I. Determinants

Chapter II. Linear spaces

Chapter III. Canonical forms of matrices and linear operators

Chapter IV. Matrices of special form

Chapter V. Multilinear algebra

Chapter VI. Matrix inequalities

Chapter VII. Matrices in algebra and calculus

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