From the reviews: "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 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
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“This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations ... . It’s also extremely well-written and logical, with short and elegant proofs. ... The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis ... and a brief summary of what is needed to extend this theory to Hilbert spaces.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)
“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 MathematikI. 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 pro¬jections.- 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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Condizione: Fair. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. Clean from markings. In fair condition, suitable as a study copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,600grams, ISBN:0387900934. Codice articolo 9847852
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Condizione: Fair. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. Book contains pencil markings. In fair condition, suitable as a study copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,600grams, ISBN:0387900934. Codice articolo 9847850
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Hardcover. Condizione: Good. Titel: Finite-Dimensional Vector Spaces. Jaar van uitgave: 1974. Taal: Engels. Rug wat verkleurd verder prima. Lichte gebruik-/opslagsporen. Lichte slijtage randjes/hoekjes/rug. Codice articolo 86650
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -From the reviews: '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 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 212 pp. Englisch. Codice articolo 9780387900933
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