A Guide To Advanced Linear Algebra
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Page Count: 266 [warning: Documents this large are best viewed by clicking the View PDF Link!]
- Front Cover
- Copyright page
- Title page
- Preface
- Contents
- 1 Vector spaces and linear transformations
- 2 Coordinates
- 3 Determinants
- 4 The structure of a linear transformation I
- 5 The structure of a linear transformation II
- 5.1 Annihilating, minimum, and characteristic polynomials
- 5.2 Invariant subspaces and quotient spaces
- 5.3 The relationship between the characteristic and minimum polynomials
- 5.4 Invariant subspaces and invariant complements
- 5.5 Rational canonical form
- 5.6 Jordan canonical form
- 5.7 An algorithm for Jordan canonical form and Jordan basis
- 5.8 Field extensions
- 5.9 More than one linear transformation
- 6 Bilinear, sesquilinear, and quadratic forms
- 7 Real and complex inner product spaces
- 8 Matrix groups as Lie groups
- Appendix A: Polynomials
- Appendix B: Modules over principal ideal domains
- Bibliography
- Index
- About the Author