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线性代数习题集（影印版）

样章
作者：
Paul R. Halmos
定价：
135.00元
ISBN：
978-7-04-055628-5
版面字数：
530.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-01
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
代数学
暂无
  • 前辅文
  • Chapter 1. Scalars
    • 1. Double addition
    • 2. Half double addition
    • 3. Exponentiation
    • 4. Complex numbers
    • 5. Affine transformations
    • 6. Matrix multiplication
    • 7. Modular multiplication
    • 8. Small operations
    • 9. Identity elements
    • 10. Complex inverses
    • 11. Affine inverses
    • 12. Matrix inverses
    • 13. Abelian groups
    • 14. Groups
    • 15. Independent group axioms
    • 16. Fields
    • 17. Addition and multiplication in fields
    • 18. Distributive failure
    • 19. Finite fields
  • Chapter 2. Vectors
    • 20. Vector spaces
    • 21. Examples
    • 22. Linear combinations
    • 23. Subspaces
    • 24. Unions of subspaces
    • 25. Spans
    • 26. Equalities of spans
    • 27. Some special spans
    • 28. Sums of subspaces
    • 29. Distributive subspaces
    • 30. Total sets
    • 31. Dependence
    • 32. Independence
  • Chapter 3. Bases
    • 33. Exchanging bases
    • 34. Simultaneous complements
    • 35. Examples of independence
    • 36. Independence over R and Q
    • 37. Independence in C2
    • 38. Vectors common to different bases
    • 39. Bases in C3
    • 40. Maximal independent sets
    • 41. Complex as real
    • 42. Subspaces of full dimension
    • 43. Extended bases
    • 44. Finite-dimensional subspaces
    • 45. Minimal total sets
    • 46. Existence of minimal total sets
    • 47. Infinitely total sets
    • 48. Relatively independent sets
    • 49. Number of bases in a finite vector space
    • 50. Direct sums
    • 51. Quotient spaces
    • 52. Dimension of a quotient space
    • 53. Additivity of dimension
  • Chapter 4. Transformations
    • 54. Linear transformations
    • 55. Domain and range
    • 56. Kernel
    • 57. Composition
    • 58. Range inclusion and factorization
    • 59. Transformations as vectors
    • 60. Invertibility
    • 61. Invertibility examples
    • 62. Determinants: 2 × 2
    • 63. Determinants: n × n
    • 64. Zero-one matrices
    • 65. Invertible matrix bases
    • 66. Finite-dimensional invertibility
    • 67. Matrices
    • 68. Diagonal matrices
    • 69. Universal commutativity
    • 70. Invariance
    • 71. Invariant complements
    • 72. Projections
    • 73. Sums of projections
    • 74. not quite idempotence
  • Chapter 5. Duality
    • 75. Linear functionals
    • 76. Dual spaces
    • 77. Solution of equations
    • 78. Reflexivity
    • 79. Annihilators
    • 80. Double annihilators
    • 81. Adjoints
    • 82. Adjoints of projections
    • 83. Matrices of adjoints
  • Chapter 6. Similarity
    • 84. Change of basis: vectors
    • 85. Change of basis: coordinates
    • 86. Similarity: transformations
    • 87. Similarity: matrices
    • 88. Inherited similarity
    • 89. Similarity: real and complex
    • 90. Rank and nullity
    • 91. Similarity and rank
    • 92. Similarity of transposes
    • 93. Ranks of sums
    • 94. Ranks of products
    • 95. Nullities of sums and products
    • 96. Some similarities
    • 97. Equivalence
    • 98. Rank and equivalence
  • Chapter 7. Canonical Forms
    • 99. Eigenvalues
    • 100. Sums and products of eigenvalues
    • 101. Eigenvalues of products
    • 102. Polynomials in eigenvalues
    • 103. Diagonalizing permutations
    • 104. Polynomials in eigenvalues, converse
    • 105. Multiplicities
    • 106. Distinct eigenvalues
    • 107. Comparison of multiplicities
    • 108. Triangularization
    • 109. Complexification
    • 110. Unipotent transformation
    • 111. Nipotence
    • 112. Nilpotent products
    • 113. Nilpotent direct sums
    • 114. Jordan form
    • 115. Minimal polynomials
    • 116. Non-commutative Lagrange interpolation
  • Chapter 8. Inner Product Spaces
    • 117. Inner products
    • 118. Polarization
    • 119. The Pythagorean theorem
    • 120. The parallelogram law
    • 121. Complete orthonormal sets
    • 122. Schwarz inequality
    • 123. Orthogonal complements
    • 124. More linear functionals
    • 125. Adjoints on inner product spaces
    • 126. Quadratic forms
    • 127. Vanishing quadratic forms
    • 128. Hermitian transformations
    • 129. Skew transformations
    • 130. Real Hermitian forms
    • 131. Positive transformations
    • 132. positive inverses
    • 133. Perpendicular projections
    • 134. Projections on C × C
    • 135. Projection order
    • 136. Orthogonal projections
    • 137. Hermitian eigenvalues
    • 138. Distinct eigenvalues
  • Chapter 9. Normality
    • 139. Unitary transformations
    • 140. Unitary matrices
    • 141. Unitary involutions
    • 142. Unitary triangles
    • 143. Hermitian diagonalization
    • 144. Square roots
    • 145. Polar decomposition
    • 146. Normal transformations
    • 147. Normal diagonalizability
    • 148. Normal commutativity
    • 149. Adjoint commutativity
    • 150. Adjoint intertwining
    • 151. Normal products
    • 152. Functions of transformations
    • 153. Gramians
    • 154. Monotone functions
    • 155. Reducing ranges and kernels
    • 156. Truncated shifts
    • 157. Non-positive square roots
    • 158. Similar normal transformations
    • 159. Unitary equivalence of transposes
    • 160. Unitary and orthogonal equivalence
    • 161. Null convergent powers
    • 162. Power boundedness
    • 163. Reduction and index 2
    • 164. Nilpotence and reduction
  • Hints
  • Solutions:
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Chapter 9

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