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