Linear Algebra: A Pure Mathematical Approach - Hardcover

Rose, H. E.

Hardcover

ISBN 10: 3764369051 ISBN 13: 9783764369057

Publisher: Birkhauser Verlag AG, 2002

Synopsis

Linear algebra is one of the most important branches of mathematics - important because of its many applications to other areas of mathematics, and important because it contains a wealth of ideas and results which are basic to pure mathematics. This book gives an introduction to linear algebra, and develops and proves its fundamental properties and theorems taking a pure mathematical approach - linear algebra contains some fine pure mathematics. Main topics: - vector spaces and algebras, dimension, linear maps, direct sums, and (briefly) exact sequences - matrices and their connections with linear maps, determinants (properties proved using some elementary group theory), and linear equations - Cayley-Hamilton and Jordan theorems leading to the spectrum of a linear map - this provides a geometric-type description of these maps - Hermitian and inner product spaces introducing some metric properties (distance, perpendicularity etc.) into the theory, also unitary and orthogonal maps and matrices - applications to finite fields, mathematical coding theory, finite matrix groups, the geometry of quadratic forms, quaternions and Cayley numbers, and some basic group representation theory A large number of examples, exercises and problems are provided. Answers and/or sketch solutions to all of the problems are given in an appendix. Some of these are theoretical and some numerical, both types are important. No particular computer algebra package is discussed but a number of the exercises are intended to be solved using one of these packages chosen by the reader.The approach is pure-mathematical, and the intended readership is undergraduate mathematicians, also anyone who requires a more than basic understanding of the subject. This book will be most useful for a "second course" in linear algebra, that is for students that have seen some elementary matrix algebra. But as all terms are defined from scratch, the book can be used for a "first course" for more advanced students.

About this title

Review

"Rose's Linear Algebra is a highly sophisticated undergraduate work . . . This book would be excellent for mathematics majors or for non-majors with access to a second course in which applications were presented. Summing Up: Recommended for lower- and upper-division undergraduates."

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"Rose's Linear Algebra is a highly sophisticated undergraduate work . . . This book would be excellent for mathematics majors or for non-majors with access to a second course in which applications were presented. Summing Up: Recommended for lower- and upper-division undergraduates."

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Synopsis

This text gives an introduction to linear algebra, developing and proving its fundamental properties and theorems taking a pure mathematical approach. It includes examples, exercises and problems, some of which are theoretical and some numerical. Answers and/or sketch solutions are given.

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 2002
• ISBN 10: 3764369051
• ISBN 13: 9783764369057
• Binding: Hardcover
• Language: English
• Number of pages: 254