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| Авторизация |
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| Поиск по указателям |
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| Wedderburn J.H.M. — Lectures on Matrices |
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| Предметный указатель |
Absolute value 125 ff. 171
Adjoint 7 66
Algebraic functions 119
Algebras 147 ff.
Algebras, basis of 148
Algebras, classification of 158
Algebras, difference 153
Algebras, division 147 159 162
Algebras, group 167
Algebras, index of 153
Algebras, matric 156 159
Algebras, matric representation of 149
Algebras, nilpotent 153
Algebras, radical of 154 157
Algebras, serai-simple 154 159 168
Algebras, simple 154 159
Associated matrix 76 ff. 96
Associated matrix, determinant of 79
Associated matrix, irreducible 85
Associative algebra 147
Automorphic transformation 140 ff. 171
Baker, H.F. 170
Basis 2 10 11 13 73 148 150
Basis, canonical 54
Basis, change of 9
Basis, fundamental 3 11
Basis, linear elementary 52
Basis, normal 49 55
Basis, orthogonal 12
Basis, reciprocal 11
Basis, unitary 13
Bibliography 172
Bibliography, index to 194
Bilinear form 9 68 128 140
Bordered determinant 67
Born, M. 135
Canonical basis 54 55
Canonical form 41 62 90
Canonical form, of a function 166
Canonical form, rational 123
Cayley 169 170 171
Chain 44 55
Characteristic 39
Characteristic equation 23 112 169
Characteristic function 23 24
Christoffel symbols 133
Classification of algebras 158
Cogredient transformation 98 ff.
Commutative matrices 20 27 102
Complement 64
Complementary subspace 3 50
COMPLEX 150
components 1
Compound matrices 64 ff.
Compound matrices, determinant of 66
Compound matrices, roots of 67
Compound matrices, supplementary 65 126
Contravariant vector 132
coordinates 1 4 72
Covariant differential operator 134
Covariant vector 132
Decomposable representation 165 ff.
definite 92 100
Degree invariants 48
Derivative 128
Derivative, covariant 135
Determinants 7 64 66 67
Determinants, bordered 67
Determinants, compound 69
Determinants, vector 73 170
Dextrolateral 115 130
Dickson, L.E. 170
Difference algebra 153
Differential 131
Differential operator 131 135
Differential operator, covariant 134
Differentiation formulae 136
Direct product 74 108 151 158
Direct product, sum 151 161
Division algebra 147 159 162
Division of polynomials 21
Divisors, elementary 38 ff. 88 92 93 105 125
Elementary divisors 38 ff. 93 105
Elementary divisors of hermitian matrix 88
Elementary divisors of matrix 39 93 125
Elementary divisors of orthogonal matrix 92
Elementary divisors of real skew-matrix 88
Elementary divisors of real symmetric matrix 88 93
Elementary divisors of unitary matrix 92
Elementary transformation 33 ff. 47 169
Elementary transformation, integral set 50
Elementary transformation, linear set 52 ff.
Elementary transformation, polynomial 21 50
Elementary transformation, set 49
Equation,  119
Equation, characteristic 23 112
Equation, reduced 24.
Equivalent 34 47 76 85 100
Equivalent, strictly 48 55 61 99
Exponential function 116 122 171
Factors, determinantal 36
Factors, invariant 36 37 52 71 107 170
Field 1 147
Forms, bilinear 9 68 128 140
Forms, hermitian 92 94
Francke 69
Frobenius 106 150 169 170
Function, algebraic 119
Function, canonical form 116
Function, characteristic 23 32
Function, exponential 116 122 171
Function, Kronecker delta 6
Function, linear vector 3
Function, logarithmic 116 122
Function, of commutative matrices 110
Function, of matric variable 115 135
Function, of matrix 26 28 29 30 115
Function, of scalar variable 128
Function, of vector variable 130 132
Function, reduced characteristic 24
Fundamental basis 3
Fundamental basis, unit matrices 5
Grade 16 73 74
Grassmann 16 64 169 170 171
Ground of matrix 15 61
Group algebra. 167
hadamard 126
Hamilton 131 169 170 171
Hamiltonian function 137
hermite 171
Hermitian forms 92 ff.
Hermitian matrices 88 ff.
Hermitian matrices, elementary divisors 88 93
Hermitian matrices, invariant vectors 90
Hermitian matrices, rank 89
Hermitian matrices, roots 88 170
Hermitian matrices, signature 95
Hilton, H. 170
Hurwitz, A. 170
Hypernumber 1 72
Idempotent elements 29 42 154 162
Idempotent matrix 7 29
identities 20 111
Identity matrix 5
Index of algebra 153
Index of chain 55
Index of nilpotent matrix 7
Induced matrix 75
Infinite products 127 171
Infinite series 115
| integral 129
Integral set 47 ff. 120
Integral set, elementary 50 52
Interpolation formula 26 28
Intersection 150
Invariant 48
Invariant, degree 48
Invariant, factors 36 38 52 71 107 170
Invariant, Kronecker 55
Invariant, of hermitian matrix 90
Invariant, subalgebra 152 161
Invariant, subspaces 166
Invariant, vectors 43 ff. 169 170
Irreducible algebra 161
Irreducible transformable sets 85
Jacobian matrix 132
kronecker 99 170
Kronecker delta function 6
Kronecker invariants 55
Kronecker reduction 96
Laevolateral 115 130
Lagrange 25 68
Laguerre 169 171
Laplace 63 66
Latent roots 24
Linear algebra 147 ff.
Linear algebra, dependence 2 10 16
Linear algebra, elementary bases 52
Linear algebra, polynomial 37 ff. 170
Linear algebra, set 2 19
Linear algebra, singular 55 ff. 170
Linear algebra, transformable 80
Linear algebra, transformation 1
Linear algebra, vector function 3
Loewy, A. 170 171
Logarithm 116 122
Matric function of scalar variable 128
Matric polynomials in scalar variable 20 21 22 24 27 29 30 33 71 115 130
Matric polynomials in scalar variable, invariant factors 36
Matric polynomials in scalar variable, linear 37 ff. 55
Matric polynomials in scalar variable, normal form 34
Matric representation of algebra 149
Matric subalgebras 156 159
Matrix 3 169
Matrix, adjoint 7
Matrix, associated 76
Matrix, compound 64
Matrix, conjugate 8
Matrix, hermitian 88
Matrix, induced 75
Matrix, Jacobian 132
Matrix, orthogonal 12
Matrix, power 75
Matrix, product transformation 75
Matrix, scalar 5 6
Matrix, skew 8 88 91
Matrix, symmetric 8 88 90
Matrix, transposed 8
Matrix, transverse 8 9
Matrix, unitary 13
McAulay, A. 135
Muir 169
Muth 170
Nilpotent algebra 153
Nilpotent matrix 7
Normal basis 49 55
Normal form 34
Nullity 15 169
NullSpace 15 43 45 69
Operator, covariant differential 134
Operator, matric differential 135
Operator, vector differential 131
Order of complex 150
Order of set 2
Orthogonal basis 12
Orthogonal matrix 12 90 91 92 142
Partial elements 42
Peano 171
Peirce 169
Permanent 75
Pole 43
Polynomial, elementary 21 50
Polynomial, linear 37 ff. 55
Polynomial, matric 20 24 25 26 33 115
Polynomial, normal form 34
Polynomial, scalar 26 28 30 106
Polynomial, vector 47 ff.
Power matrix 75
Powers of matrix 6 26 120
Primitive idempotent element 155 162
Principal idempotent elements 29
Principal nilpotent elements 29
Principal unit 147 155
Product of complexes 150
Product, direct 74 108 151 158
Product, infinite 127 171
Product, of matrices 4
Product, of tensors 72
Product, scalar 9 63
Product, transformation 75
Quasi-hermitian forms 92 ff.
Quasi-orthogonal 93
Radical 154 157
Rados 170
Rank 14 16 34 -69 96 169
Rank, hermitian matrix 89 94
Reciprocal bases 11
Reduced characteristic function 24 32
Reduced equation 24
Reducible matrix 31 77
Reducible matrix, representation 165 167
Reduction of bilinear forms 68
Reduction of hermitian forms 93 96
Reduction of quadratic forms 93 96
Regular matrix 7
Regular matrix, representation 166 167
Remainder theorem 22 169
Representation of algebra 149 165
Roots of associated matrix 79
Roots of associated matrix, commutative matrices 111
Roots of associated matrix, compound matrix 67
Roots of associated matrix, matric function 26 29 30 111
Roots of associated matrix, matrix 24 27
Roots of associated matrix, orthogonal matrix 91
Roots of associated matrix, permitian matrix 88 170
Roots of associated matrix, skew matrix 91 170
Roots of associated matrix, symmetric matrix 88 170
Roots of associated matrix, unitary matrix 91
scalar 1 9 63 81
Scalar matrix 5 6
Scalar polynomials 26 28 30
Schur, I. 170
Semi-definite 92
Semi-simple algebra 154 158 168
Series, infinite 115
Set, elementary 49 52 55
Set, integral 47 ff.
Set, linear 2 19
Set, order of 2
Set, transformable 80 85
Signature 95 100
Similar matrices 11 25 38 41 113 141
Similar matrices, linear elementary sets 55
Simple algebra 154 ff.
singular 7 158
Skew matrix 8 93 96 99 142
Skew matrix, real 88 91
smith 170
Square root 30 118 169
Stephanos 170
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