Advanced Linear Algebra

Authors:

ISBN: 978-0-387-24766-3 (Print) 978-0-387-27474-4 (Online)

Table of contents (19 chapters)

  1. Preliminaries

    1. No Access

      Book Chapter

      Pages 1-30

      Preliminaries

  2. Basic Linear Algebra

    1. Front Matter

      Pages 31-31

    2. No Access

      Book Chapter

      Pages 33-54

      Vector Spaces

    3. No Access

      Book Chapter

      Pages 55-74

      Linear Transformations

    4. No Access

      Book Chapter

      Pages 75-91

      The Isomorphism Theorems

    5. No Access

      Book Chapter

      Pages 93-108

      Modules I: Basic Properties

    6. No Access

      Book Chapter

      Pages 109-120

      Modules II: Free and Noetherian Modules

    7. No Access

      Book Chapter

      Pages 121-140

      Modules over a Principal Ideal Domain

    8. No Access

      Book Chapter

      Pages 141-152

      The Structure of a Linear Operator

    9. No Access

      Book Chapter

      Pages 153-179

      Eigenvalues and Eigenvectors

    10. No Access

      Book Chapter

      Pages 181-199

      Real and Complex Inner Product Spaces

    11. No Access

      Book Chapter

      Pages 201-235

      Structure Theory for Normal Operators

  3. Topics

    1. Front Matter

      Pages 237-237

    2. No Access

      Book Chapter

      Pages 239-282

      Metric Vector Spaces: The Theory of Bilinear Forms

    3. No Access

      Book Chapter

      Pages 283-306

      Metric Spaces

    4. No Access

      Book Chapter

      Pages 307-335

      Hilbert Spaces

    5. No Access

      Book Chapter

      Pages 337-393

      Tensor Products

    6. No Access

      Book Chapter

      Pages 395-408

      Positive Solutions to Linear Systems: Convexity and Separation

    7. No Access

      Book Chapter

      Pages 409-423

      Affine Geometry

    8. No Access

      Book Chapter

      Pages 425-436

      Operator Factorizations: QR and Singular Value

    9. No Access

      Book Chapter

      Pages 437-472

      The Umbral Calculus