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Finite-dimensional vector spaces/ Paul R. Halmos

By: Halmons, Paul RMaterial type: Text

TextSeries: (University series in undergraduate mathematics)Publication details: New York: Springer, 1993Description: vii, 200 p. ; 24 cmISBN: 9780387900933Subject(s): Transformations (Mathematics) | Vector spaces | Logic, Symbolic and mathematical | Mathematical models | Generalized spaces | Vector analysis | Algebras, LinearDDC classification: 512.52

Contents:

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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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	512.52 HAL/F (Browse shelf(Opens below))	Available		P06404

Total holds: 0

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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