Finite-dimensional vector spaces / by Paul R. Halmos.
Series The university series in undergraduate mathematicsEditor: Princeton, New Jersey : D. van Nostrand, c1958Edición: 2nd edDescripción: viii, 200 p. ; 24 cmOtra clasificación: 15-01 (47-01)CONTENTS CHAPTER PAGE I. SPACES [1] 1. Fields, [1] ; 2. Vector spaces, [3] ; 3. Examples, [4] ; 4. Comments, [5] ; 5. Linear dependence, [7] ; 6. Linear combinations, [9] ; 7. Bases, [10] ;8. Dimension, [13] ; 9. Isomorphism, [14] ; 10. Subspaces, [16] ; 11. Calculus of subspaces, [17] ; 12. Dimension of a subspace, [18] ; 13. Dual spaces, [20] ; 14. Brackets, [21] ; 15. Dual bases, [23] ; 16.Reflexivity, [24] ; 17. Annihilators, [26] ; 18. Direct sums, [28] ; 19. Dimension of a direct sum, [30] ; 20. Dual of a direct sum, [31] ; 21. Quotient spaces, [33] ; 22. Dimension of a quotient space, [34] ; 23. Bilinear forms, [35] ; 24. Tensor products, [38] ; 25. Product bases, [40] ; 26. Permutations, [41] ; 27. Cycles, [44] ; 28. Parity, [46] ; 29. Multilinear forms, [48] ; 30. Alternating forms, [50] ; 31. Alternating forms of maximal degree, [52] II. TRANSFORMATIONS [55] 32. Linear transformations, [55] ; 33. Transformations as vectors, [56] ; 34. Products, [58] ; 35. Polynomials, [59] ; 36. Inverses, [61] ; 37. Matrices, [64] ; 38. Matrices of transformations, [67] ; 39. Invariance, [71] ; 40. Reducibility, [72] ; 41. Projections, [73] ; 42. Combinations of projections, [74] ; 43. Projections and invariance, [76] ; 44. Adjoints, [78] ; 45. Adjoints of projections, [80] ; 46. Change of basis, [82] ; 47. Similarity, [84] ; 48. Quotient transformations, [87] ; 49. Range and nullspace, [88] ; 50. Rank and nullity, [90] ; 51. Transformations of rank one, [92] ; 52. Tensor products of transformations, [95] ; 53. Determinants, [98] ; 54. Proper values, [102] ; 55. Multiplicity, [104] ; 56. Triangular form, [106] ; 57. Nilpotence, [109] ; 58. Jordan form, [112] III. ORTHOGONALITY [118] 59. Inner products, [118] ; 60. Complex inner products, [120] ; 61. Inner product spaces, [121] ; 62. Orthogonality, [122] ; 63. Completeness, [124] ; 64. Schwarz’s inequality, [125] ; 65. Complete orthonormal sets, [127]
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CONTENTS --
CHAPTER PAGE --
I. SPACES [1] --
1. Fields, [1] --
; 2. Vector spaces, [3] --
; 3. Examples, [4] --
; 4. Comments, [5] --
; 5. Linear dependence, [7] --
; 6. Linear combinations, [9] --
; 7. Bases, [10] --
;8. Dimension, [13] --
; 9. Isomorphism, [14] --
; 10. Subspaces, [16] --
; 11. Calculus of subspaces, [17] --
; 12. Dimension of a subspace, [18] --
; 13. Dual spaces, [20] --
; 14. Brackets, [21] --
; 15. Dual bases, [23] --
; 16.Reflexivity, [24] --
; 17. Annihilators, [26] --
; 18. Direct sums, [28] --
; 19. Dimension of a direct sum, [30] --
; 20. Dual of a direct sum, [31] --
; 21. Quotient spaces, [33] --
; 22. Dimension of a quotient space, [34] --
; 23. Bilinear forms, [35] --
; 24. Tensor products, [38] --
; 25. Product bases, [40] --
; 26. Permutations, [41] --
; 27. Cycles, [44] --
; 28. Parity, [46] --
; 29. Multilinear forms, [48] --
; 30. Alternating forms, [50] --
; 31. Alternating forms of maximal degree, [52] --
II. TRANSFORMATIONS [55] --
32. Linear transformations, [55] --
; 33. Transformations as vectors, [56] --
; 34. Products, [58] --
; 35. Polynomials, [59] --
; 36. Inverses, [61] --
; 37. Matrices, [64] --
; 38. Matrices of transformations, [67] --
; 39. Invariance, [71] --
; 40. Reducibility, [72] --
; 41. Projections, [73] --
; 42. Combinations of projections, [74] --
; 43. Projections and invariance, [76] --
; 44. Adjoints, [78] --
; 45. Adjoints of projections, [80] --
; 46. Change of basis, [82] --
; 47. Similarity, [84] --
; 48. Quotient transformations, [87] --
; 49. Range and nullspace, [88] --
; 50. Rank and nullity, [90] --
; 51. Transformations of rank one, [92] --
; 52. Tensor products of transformations, [95] --
; 53. Determinants, [98] --
; 54. Proper values, [102] --
; 55. Multiplicity, [104] --
; 56. Triangular form, [106] --
; 57. Nilpotence, [109] --
; 58. Jordan form, [112] --
III. ORTHOGONALITY [118] --
59. Inner products, [118] --
; 60. Complex inner products, [120] --
; 61. Inner product spaces, [121] --
; 62. Orthogonality, [122] --
; 63. Completeness, [124] --
; 64. Schwarz’s inequality, [125] --
; 65. Complete orthonormal sets, [127] --
MR, 19,725b
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