Finite-dimensional vector spaces/ Paul R. Halmos
Material type:
TextSeries: (University series in undergraduate mathematics)Publication details: New York: Springer, 1993.Description: vii, 200 p. ; 24 cmISBN: - 9780387900933
- 512.52 HAL/F
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General Books
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Central Library, Sikkim University General Book Section | 512.52 HAL/F (Browse shelf(Opens below)) | Available | P06404 |
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| 512.5 TOL/ From vector to tensor/ | 512.5028553 ARA/E Exploring linear algebra./ | 512.5078553042 DEE/I Interactive Linear Algebra with Maple V/ | 512.52 HAL/F Finite-dimensional vector spaces/ | 512.52 HAL/F Finite dimensional vector spaces/ | 512.52 HAL/F Finite dimensional vector spaces/ | 512.522 SHI/M Modular forms: basics and beyond/ |
I. Spaces.-
1. Fields.-
2. Vector spaces.-
3. Examples.-
4. Comments.-
5. Linear dependence.-
6. Linear combinations.-
7. Bases.-
8. Dimension.-
9. Isomorphism.-
10. Subspaces.-
11. Calculus of subspaces.-
12. Dimension of a subspace.-
13. Dual spaces.-
14. Brackets.-
15. Dual bases.-
16. Reflexivity.-
17. Annihilators.-
18. Direct sums.-
19. Dimension of a direct sum.-
20. Dual of a direct sum.-
21. Quotient spaces.-
22. Dimension of a quotient space.-
23. Bilinear forms.-
24. Tensor products.-
25. Product bases.-
26. Permutations.-
27. Cycles.-
28. Parity.-
29. Multilinear forms.-
30. Alternating forms.-
31. Alternating forms of maximal degree.-
II. Transformations.-
32. Linear transformations.-
33. Transformations as vectors.-
34. Products.-
35. Polynomials.-
36. Inverses.-
37. Matrices.-
38. Matrices of transformations.-
39. Invariance.-
40. Reducibility.-
41. Projections.-
42. Combinations of projections.-
43. Projections and invariance.-
44. Adjoints.-
45. Adjoints of projections.-
46. Change of basis.-
47. Similarity.-
48. Quotient transformations.-
49. Range and null-space.-
50. Rank and nullity.-
51. Transformations of rank one.-
52. Tensor products of transformations.-
53. Determinants.-
54. Proper values.-
55. Multiplicity.-
56. Triangular form.-
57. Nilpotence.-
58. Jordan form.-
III. Orthogonality.-
59. Inner products.-
60. Complex inner products.-
61. Inner product spaces.-
62. Orthogonality.-
63. Completeness.-
64. Schwarz's inequality.-
65. Complete orthonormal sets.-
66. Projection theorem.-
67. Linear functionals.-
68. Parentheses versus brackets.-
69. Natural isomorphisms.-
70. Self-adjoint transformations.-
71. Polarization.-
72. Positive transformations.-
73. Isometries.-
74. Change of orthonormal basis.-
75. Perpendicular projections.-
76. Combinations of perpendicular projections.-
77. Complexification.-
78. Characterization of spectra.-
79. Spectral theorem.-
80. Normal transformations.-
81. Orthogonal transformations.-
82. Functions of transformations.-
83. Polar decomposition.-
84. Commutativity.-
85. Self-adjoint transformations of rank one.-
IV. Analysis.-
86. Convergence of vectors.-
87. Norm.-
88. Expressions for the norm.-
89. Bounds of a self-adjoint transformation.-
90. Minimax principle.-
91. Convergence of linear transformations.-
92. Ergodic theorem.-
93. Power series.-
Appendix.
Hilbert Space.-
Recommended Reading.-
Index of Terms.-
Index of Symbols
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