UID:
almahu_9947362969802882
Umfang:
VIII, 202 p.
,
online resource.
ISBN:
9781461263876
Serie:
Undergraduate Texts in Mathematics,
Inhalt:
“The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other “modern” textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher.” Zentralblatt für Mathematik.
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9781461263890
Sprache:
Englisch
DOI:
10.1007/978-1-4612-6387-6
URL:
http://dx.doi.org/10.1007/978-1-4612-6387-6
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