Neuware - Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives. Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups. The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.

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Bibliographic Details

Title

A Guide to Advanced Linear Algebra

Publisher

Mathematical Association Of America (MAA) Jul 2011

Publication Date

2011

Language

English

ISBN 10

0883853515

ISBN 13

9780883853511

Binding

Buch

Condition

Neu

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Synopsis

The core of linear algebra is essential to most mathematicians. This book is ideal for graduate students and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.

About the Author

Steven H. Weintraub is Professor of Mathematics at Lehigh University. He is the author of over fifty research papers and this is his ninth book.

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