2007

The Linear Algebra a Beginning Graduate Student Ought to Know

Authors:

ISBN: 978-1-4020-5494-5 (Print) 978-1-4020-5495-2 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages I-XI

  2. No Access

    Book Chapter

    Pages 1-3

    Notation and terminology

  3. No Access

    Book Chapter

    Pages 5-16

    Fields

  4. No Access

    Book Chapter

    Pages 17-32

    Vector spaces over a field

  5. No Access

    Book Chapter

    Pages 33-48

    Algebras over a field

  6. No Access

    Book Chapter

    Pages 49-78

    Linear independence and dimension

  7. No Access

    Book Chapter

    Pages 79-98

    Linear transformations

  8. No Access

    Book Chapter

    Pages 99-116

    The endomorphism algebra of a vector space

  9. No Access

    Book Chapter

    Pages 117-130

    Representation of linear transformations by matrices

  10. No Access

    Book Chapter

    Pages 131-168

    The algebra of square matrices

  11. No Access

    Book Chapter

    Pages 169-198

    Systems of linear equations

  12. No Access

    Book Chapter

    Pages 199-228

    Determinants

  13. No Access

    Book Chapter

    Pages 229-266

    Eigenvalues and eigenvectors

  14. No Access

    Book Chapter

    Pages 267-284

    Krylov subspaces

  15. No Access

    Book Chapter

    Pages 285-298

    The dual space

  16. No Access

    Book Chapter

    Pages 299-324

    Inner product spaces

  17. No Access

    Book Chapter

    Pages 325-348

    Orthogonality

  18. No Access

    Book Chapter

    Pages 349-368

    Selfadjoint Endomorphisms

  19. No Access

    Book Chapter

    Pages 369-388

    Unitary and Normal endomorphisms

  20. No Access

    Book Chapter

    Pages 389-398

    Moore-Penrose pseudoinverses

  21. No Access

    Book Chapter

    Pages 399-422

    Bilinear transformations and forms

  22. Back Matter

    Pages 423-435