Advanced Linear Algebra

Authors:

ISBN: 978-0-387-72828-5 (Print) 978-0-387-72831-5 (Online)

Table of contents (19 chapters)

  1. Front Matter

    Pages I-XVIII

  2. Basic Linear Algebra

    1. Front Matter

      Pages 33-33

    2. No Access

      Book Chapter

      Pages 35-58

      Vector Spaces

    3. No Access

      Book Chapter

      Pages 59-85

      Linear Transformations

    4. No Access

      Book Chapter

      Pages 87-107

      The Isomorphism Theorems

    5. No Access

      Book Chapter

      Pages 109-126

      Modules I: Basic Properties

    6. No Access

      Book Chapter

      Pages 127-138

      Modules II: Free and Noetherian Modules

    7. No Access

      Book Chapter

      Pages 139-161

      Modules over a Principal Ideal Domain

    8. No Access

      Book Chapter

      Pages 163-184

      The Structure of a Linear Operator

    9. No Access

      Book Chapter

      Pages 185-203

      Eigenvalues and Eigenvectors

    10. No Access

      Book Chapter

      Pages 205-226

      Real and Complex Inner Product Spaces

    11. No Access

      Book Chapter

      Pages 227-255

      Structure Theory for Normal Operators

  3. Topics

    1. Front Matter

      Pages 257-257

    2. No Access

      Book Chapter

      Pages 259-300

      Metric Vector Spaces: The Theory of Bilinear Forms

    3. No Access

      Book Chapter

      Pages 301-324

      Metric Spaces

    4. No Access

      Book Chapter

      Pages 325-353

      Hilbert Spaces

    5. No Access

      Book Chapter

      Pages 355-409

      Tensor Products

    6. No Access

      Book Chapter

      Pages 411-425

      Positive Solutions to Linear Systems: Convexity and Separation

    7. No Access

      Book Chapter

      Pages 427-441

      Affine Geometry

    8. No Access

      Book Chapter

      Pages 443-450

      Singular Values and the Moore–Penrose Inverse

    9. No Access

      Book Chapter

      Pages 451-470

      An Introduction to Algebras

    10. No Access

      Book Chapter

      Pages 471-506

      The Umbral Calculus

  4. Back Matter

    Pages 507-526