Index Adjoint of a matrix, 112 of an operator, 63, 112 Algebra, 200 Alternating form, 72 Annihilator, 59 Automorphism, 7 Axiom of choice, 20 Basic partition, 175 Basis, 15 dual, 58 standard, 17 Bilinear form, 59, 63, 69 map, 69 Canonical prime-power decomposition, 140 Cauchy-Schwarz, 105 Cayley-Hamilton, 95 Character, 124 Characteristic polynomial of a matrix, 86 of an operator, 85 Codimension, 18 Cofactor, 80 Complement, 11 Composition, 39 Congruent matrices, 163 Conjugate matrices, 43 operators, 40 Conjugation group actions, 196 in S„, 67 Connecting chain, 171 Contraction, 132 Coset, 10, 192 Cycle, 65, 66 Cyclic decomposition, 152 system, 94 vector, 94 Decomposition cyclic, 150, 152 general], 138 prime power, 140 Degrees of freedom, 28 Determinant of a matrix, 79 of an operator, 76 Diagonal matrix, 44 Diagonal sum, 81,136 Diagonalizable, 49 Dimension, 17, 18 Direct sum formal, 1 0 of subspaces, 11 Eigenspace, 86 generalized, 142 Eigenvalue, 64, 86, 89 Eigenvector, 64, 86, 89 dominant, 168 211

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