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| Авторизация |
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| Katznelson I., KatznelsonY.R. — A (Terse) Introduction to Linear Algebra (Student Mathematical Library) |
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| Предметный указатель |
Adjoint of a matrix 112
Adjoint of an operator 63 112
Algebra 200
Alternating form 72
Annihilator 59
Automorphism 7
Axiom of Choice 20
Basic partition 175
Basis 15
Basis, dual 58
Basis, standard 17
Bilinear form 59 63 69
Bilinear map 69
Canonical prime-power decomposition 140
Cauchy — Schwarz 105
Cayley — Hamilton 95
CHARACTER 124
Characteristic polynomial of a matrix 86
Characteristic polynomial of an operator 85
Codimension 18
Cofactor 80
Complement 11
composition 39
Congruent matrices 163
Conjugate matrices 43
Conjugate operators 40
Conjugation in  67
Conjugation, group actions 196
Connecting chain 171
Contraction 132
Coset 10 192
CYCLE 65 66
Cyclic decomposition 152
Cyclic system 94
Cyclic vector 94
Decomposition, cyclic 150 152
Decomposition, general 138
Decomposition, prime power 140
Degrees of freedom 28
Determinant of a matrix 79
Determinant of an operator 76
Diagonal matrix 44
Diagonal sum 81 136
Diagonalizable 49
DIMENSION 17 18
Direct sum of subspaces 11
Direct sum, formal 10
Eigenspace 86
Eigenspace, generalized 142
Eigenvalue 64 86 89
Eigenvector 64 86 89
Eigenvector, dominant 168
Elementary divisors 155
Equivalence relation 187
Euclidean space 103
Factorization in ![$\mathbb{R}[x]$](/math_tex/f15addcc8ab3f7f3bd7b44966280b59582.gif) 206
Factorization, prime-power 140 141 204
Field 2
Field, extension 200
Fixed point 65
Flag 92
Fourier expansion 125
Frobenius 175
Gauss — Jordan elimination 26
Gaussian elimination 24
Group 1 189
Group, abelian 1
Group, cyclic 192
Group, dual 125
Group, general linear 40 43
Hadamard's inequality 110
Hamel basis 20
Hermitian form 103 163
Ideal 197
Idempotent 41 110
Independent subspaces 11 13
Independent vectors 14
Inertia, law of 165
Inner product 103
Irreducible, polynomial 203
Irreducible, system 135
Isomorphism 6
Jordan canonical form 151 156
k-form 69
Kernel 51
Lagrange 62
linear combination 9
Linear equations, homogeneous 22
Linear equations, nonhomogeneous 22
Linear operator 35
Linear system 40 49
Markov chain 178
Markov chain, reversible 179
Matrix, augmented 25
Matrix, companion 96
Matrix, derogatory 97
Matrix, diagonal 9
Matrix, hermitian 113
Matrix, integral 82
Matrix, nonderogatory 97
Matrix, nonnegative 166 170
Matrix, orthogonal 122
Matrix, permutation 44
Matrix, positive 167
Matrix, self-adjoint 113
Matrix, skew-symmetric 9
Matrix, stochastic 178
Matrix, strongly transitive 175
Matrix, symmetric 8
Matrix, transitive 171
Matrix, triangular 9 81 92
Matrix, unimodular 82
Matrix, unipotent 151
Matrix, unitary 122
| Minimal polynomial 96
Minimal polynomial for  93
Minimal system 100
Minmax principle 118
Monic polynomial 201
Multilinear form 69
Multilinear map 69
Nilpotent 147
Nilspace 142
Norm of an operator 56
Norm on a vector space 32
Normal operator 119
Nullity 51
NullSpace 52
Operator, derogatory 97
Operator, induced on a quotient 78
Operator, linear 35
Operator, nonderogatory 97
Operator, nonnegative definite 127
Operator, nonsingular 52
Operator, normal 119
Operator, orthogonal 121
Operator, positive definite 127
Operator, self-adjoint 113
Operator, singular 52
Operator, unitary 121
Order element 192
Order group 189
Orientation 77
Orthogonal equivalence 122
Orthogonal operator 121
Orthogonal projection 108
Orthogonal vectors 106
Orthonormal 106
Period group 174
periodicity 174
Permutation 65 189
Permutation matrix 44
Perron 168
Pivot column 26
Polar decomposition 128
Polarization 111
Primary components 140
Probability vector 178
Projection 41
Projection, along a subspace 36
Projection, orthogonal 108
Quadratic form 162
Quadratic form, positive definite 165
Quotient space 9
RANGE 51
Rank of a matrix 29
Rank of an operator 51
Rank, column 29
Rank, row 25
Reduced-row-echelon form 26
Reducing subspace 135
Regular representation 185
Representation 181
Representation, equivalent 182
Representation, faithful 181
Representation, reducible 184
Representation, regular 185
Representation, unitary 181
Restriction of an operator 78
Return times 171
Ring 196
Row equivalence 25
Schur decomposition 123
Schur's lemma 100
Self-adjoint algebra 117
Self-adjoint operator 113
Semisimple algebra 144
Semisimple system 142
Shift, k-shift 148
Shift, standard 148
Similar matrices 49
Similar operators 49
Singular value decomposition 131
Singular values 130
Solution-set 8 23
span 9 14
Spectral mapping theorem 89
Spectral norm 162 167
Spectral theorems 114—120
Spectrum 89 141
Spectrum of a matrix 86
Spectrum of an operator 85
Spectrum, joint 117
Square-free 143
Steinitz' lemma 17
Stochastic 178
Subalgebra 200
Subgroup, index 192
Subgroup, normal 193
SubMatrix 30
Submatrix, principal 30
Support 167
Sylvester matrix 32
Symmetric form 72
Symmetric group 65
Tensor product 12
Trace 87
Transition matrix 178
Transposition 66
Unitary dilation 132
Unitary equivalence 122
Unitary group 183
Unitary operator 121
Unitary space 103
Vandermonde 82
Vector space 4
Vector space, complex 4
Vector space, real 4
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