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Contents 8 Preface 6 Chapter I. Vector Spaces 10 1. Fields 11 Problems 16 2. Vector Spaces 18 Problems 24 3. Subspaces 26 Problems 31 4. Spanning and Linear Independence 33 Problems 38 5. The Replacement Theorem 40 Problems 46 6. Matrices and Elementary Operations 48 Problems 53 7. Linear Equations and Bases 55 Problems 60 Chapter II. Linear Transformations 62 8. Linear Transformations 63 Problems 69 9. Kernels and Images 70 Problems 75 10. Quotient Spaces 77 Problems 83 11. Matrix Correspondence 86 Problems 93 12. Products of Linear Transformations 95 Problems 102 13. Eigenvalues and Eigenvectors 104 Problems 110 Chapter III. Determinants 112 14. Volume Functions 113 Problems 121 15. Determinants 123 Problems 130 16. Consequences of Uniqueness 132 Problems 140 17. Adjoints and Inverses 142 Problems 150 18. The Characteristic Polynomial 151 Problems 157 19. The Cayley-Hamilton Theorem 159 Problems 164 20. Nilpotent Transformations 166 Problems 172 21. Jordan Canonical Form 174 Problems 178 Chapter IV. Bilinear Forms 180 22. Bilinear Forms 181 Problems 185 23. Symmetric and Skew-Symmetric Forms 187 Problems 191 24. Congruent Matrices 193 Problems 197 25. Inner Product Spaces 199 Pro

Author

Donald S Passman

Language

EN