Author(s): I. M. Gel'fand
Publisher: Dover Publications
Year: 1989
Language: English
Pages: 190
Table of Contents......Page 5
Preface to the second edition......Page 3
Preface to the first edition......Page 4
§1. n-Dimensional vector spaces......Page 6
§2. Euclidean space......Page 19
§3. Orthogonal basis. Isomorphism of Euclidean spaces......Page 26
§4. Bilinear and quadratic forms......Page 39
§5. Reduction of a quadratic form to a sum of squares......Page 47
§6. Reduction of a quadratic form by means of a triangular transformation......Page 51
§7. The law of inertia......Page 60
§8. Complex n-dimensional space......Page 65
§9. Linear transformations. Operations on linear transformations......Page 75
§10. Invariant subspaces. Eigenvalues and eigenvectors of a linear transformation......Page 86
§11. The adjoint of a linear transformation......Page 95
§12. Self-adjoint (Hermitian) transformations. Simultaneous reduction of a pair of quadratic forms to a sum of squares......Page 102
§13. Unitary transformations......Page 108
§14. Commutative linear transformations. Normal transformations......Page 112
§15. Decomposition of a linear transformation into a product of a unitary and self-adjoint transformation......Page 116
§16. Linear transformations on a real Euclidean space......Page 119
§17. Extremal properties of eigenvalues......Page 131
§18. The canonical form of a linear transformation......Page 137
§19. Reduction to canonical form......Page 142
§20. Elementary divisors......Page 147
§21. Polynomial matrices......Page 154
§22. The dual space......Page 169
§23. Tensors......Page 176
