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Advanced Linear Algebra

  • Steven┬áRoman

Part of the Graduate Texts in Mathematics book series (GTM, volume 135)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Preliminaries

    1. Steven Roman
      Pages 1-24
  3. Basic Linear Algebra

    1. Front Matter
      Pages 25-25
    2. Steven Roman
      Pages 27-43
    3. Steven Roman
      Pages 45-62
    4. Steven Roman
      Pages 63-81
    5. Steven Roman
      Pages 83-95
    6. Steven Roman
      Pages 97-106
    7. Steven Roman
      Pages 107-119
    8. Steven Roman
      Pages 121-133
    9. Steven Roman
      Pages 135-156
    10. Steven Roman
      Pages 157-174
    11. Steven Roman
      Pages 175-202
  4. Topics

    1. Front Matter
      Pages 203-203
    2. Steven Roman
      Pages 205-237
    3. Steven Roman
      Pages 239-261
    4. Steven Roman
      Pages 263-290
    5. Steven Roman
      Pages 291-314
    6. Steven Roman
      Pages 315-328
    7. Steven Roman
      Pages 329-352
  5. Back Matter
    Pages 353-366

About this book

Introduction

This book is a thorough introduction to linear algebra, for the graduate or advanced undergraduate student. Prerequisites are limited to a knowledge of the basic properties of matrices and determinants. However, since we cover the basics of vector spaces and linear transformations rather rapidly, a prior course in linear algebra (even at the sophomore level), along with a certain measure of "mathematical maturity," is highly desirable. Chapter 0 contains a summary of certain topics in modern algebra that are required for the sequel. This chapter should be skimmed quickly and then used primarily as a reference. Chapters 1-3 contain a discussion of the basic properties of vector spaces and linear transformations. Chapter 4 is devoted to a discussion of modules, emphasizing a comparison between the properties of modules and those of vector spaces. Chapter 5 provides more on modules. The main goals of this chapter are to prove that any two bases of a free module have the same cardinality and to introduce noetherian modules. However, the instructor may simply skim over this chapter, omitting all proofs. Chapter 6 is devoted to the theory of modules over a principal ideal domain, establishing the cyclic decomposition theorem for finitely generated modules. This theorem is the key to the structure theorems for finite dimensional linear operators, discussed in Chapters 7 and 8. Chapter 9 is devoted to real and complex inner product spaces.

Keywords

Eigenvalue Eigenvector algebra linear algebra matrices transformation

Authors and affiliations

  • Steven┬áRoman
    • 1
  1. 1.Department of MathematicsCalifornia State University at FullertonFullertonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2178-2
  • Copyright Information Springer-Verlag New York 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-2180-5
  • Online ISBN 978-1-4757-2178-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site