Linear Algebra and Geometry

  • Igor R. Shafarevich
  • Alexey O. Remizov

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Igor R. Shafarevich, Alexey O. Remizov
    Pages 1-23
  3. Igor R. Shafarevich, Alexey O. Remizov
    Pages 25-77
  4. Igor R. Shafarevich, Alexey O. Remizov
    Pages 79-131
  5. Igor R. Shafarevich, Alexey O. Remizov
    Pages 133-160
  6. Igor R. Shafarevich, Alexey O. Remizov
    Pages 161-189
  7. Igor R. Shafarevich, Alexey O. Remizov
    Pages 191-212
  8. Igor R. Shafarevich, Alexey O. Remizov
    Pages 213-288
  9. Igor R. Shafarevich, Alexey O. Remizov
    Pages 289-317
  10. Igor R. Shafarevich, Alexey O. Remizov
    Pages 319-347
  11. Igor R. Shafarevich, Alexey O. Remizov
    Pages 349-383
  12. Igor R. Shafarevich, Alexey O. Remizov
    Pages 385-432
  13. Igor R. Shafarevich, Alexey O. Remizov
    Pages 433-465
  14. Igor R. Shafarevich, Alexey O. Remizov
    Pages 467-495
  15. Igor R. Shafarevich, Alexey O. Remizov
    Pages 497-514
  16. Back Matter
    Pages 515-526

About this book

Introduction

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Keywords

groups, rings, modules linear algerba matrix projective space vector space

Authors and affiliations

  • Igor R. Shafarevich
    • 1
  • Alexey O. Remizov
    • 2
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.CMAP, École Polytechnique CNRSPalaiseau CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-30994-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-30993-9
  • Online ISBN 978-3-642-30994-6
  • About this book