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. Its main topics include: 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; and, a large number of examples, exercises and problems are provided. It gives answers and/or sketch solutions to all of the problems 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, this 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
• Language: English
• ISBN 10: 3764369051
• ISBN 13: 9783764369057
• Binding: Hardcover
• Number of pages: 254