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| Turnbull H.W. — An Introduction to the Theory of Canonical Matrices |
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| Предметный указатель |
Matrix, associate 32—33
Matrix, augmented 29—30
Matrix, auxiliary unit 62
Matrix, compound 27 73 90 93 98 180
Matrix, congruence modulo 22
Matrix, conjugate 32—33
Matrix, defined 1
Matrix, determinant of 3
Matrix, diagonal 7 8
Matrix, difference-product 77—78 149
Matrix, elementary 48 62
Matrix, equations 143 145 148 166
Matrix, equivalent 19
Matrix, functions of 7 73 81 149 151
Matrix, hermitian 32—33
Matrix, induced 183
Matrix, infinite 166 178
Matrix, invariant factors of 54
Matrix, involutory 32—33
Matrix, latent 106
Matrix, latent roots of 41 44
Matrix, non-singular 4
Matrix, null 2
Matrix, orthogonal and unitary 32—33 100 105 108 109 181 185
Matrix, partitioned 5
Matrix, polar co-ordinates of 185
Matrix, pure imaginary 33—34
Matrix, R.C.F. and R.C.E. of 48
Matrix, rank of 27 30 40 80
Matrix, reciprocal or inverse 4
Matrix, rectangular 2 9
Matrix, scalar 4
Matrix, secondary unit 11 151 152
Matrix, singular 4
Matrix, skew Hermitian and symmetric 33 98 133
Matrix, symmetric 11 15 32 152 164—165
Matrix, transposed 2
Matrix, unit 2
Matrix, unitary See orthogonal
Maxima and minima 168—169
Maxima and minima, of quadratic forms 167—168 169 178 183
Maxima and minima, under conditions 170
Mean values 176
Minimal indices 119 120—121
Minimal indices, submatrrces 121
Minimal indices, vectors 124
Minors, H.C.F. of 25
Minors, inequalities in 98
Minors, of indefinite matrix 101
Moments, in statistical sample 175—176
Moments, quadratic 174
Muir 11 31 56 81 99 112 178
Multiplication, compound 27 90 93 98
Multiplication, matrix 3 16
Multiplication, partitioned 6
Multiplication, scalar 2
Mumaghan 185
Muth 142
Nicoletti 56
Non-commutative law 3 4
Non-commutative law, algebra 143
Non-singular matrix 4
Non-singular matrix, pencil 114
Norm of vector 39
Normal equations 173
Normal equations, frequency 174—175
Nucleus 66
Null matrix 2
Nullity 40 80
Object points 40
orthogonal matrices 32—35 100 105—106 110 160 181
Orthogonal matrices, properties of partial resolvents 163—164 166
Orthogonalizing process 95—96
Orthogonant of Cayley 107 112
Pairs of forms 106—107 171
Partial equivalence 129
Partial equivalence, resolvents 163—164 166
Partitioned matrices 5
Partitions, conjugate 80
Pascal triangle 156
Pencils of conies 115 118 182
Pencils of conies, of forms 114 131
Pencils of conies, of matrices 113
Pencils of conies, of quadratics 131—132 182
Pencils, elementary divisors of 117 136
Pencils, invariant factors of 116—117 119
Pencils, on transposed matrices, based 135—136 142
Pencils, rational and classical 115—116
Pencils, rational Hermitian canonical 133—134 141 142
Pencils, singular and non-singular 114 125
Pencils, singular Hermitian and quadratic 131 134
Pencils, singular, of bilinear forms 129—130
Pencils, skew symmetric 133
Permutable matrices 166 180
Permutation, self-conjugate 11
Phillips, H. B. 166 180
Point vector 2 3
Point vector, latent 40 41 44
Polar co-ordinates of a matrix 185
Polarization 84
Poles 40 41
Polynomials, H.C.F. of 16 21—22
Polynomials, matrix 23
Polynomials, orthogonal 102
Postmultiplication 2 16
potential energy 171
Premultiplication 3
Prime vector 2
Prime vector, latent 154
Quadratic forms 15 89—90 106
Quadratic forms, compound 91
Quadratic forms, families of 30
Quadratic forms, latent 154
Quadratic forms, pairs of 106—107
Quadratic forms, pencils 130—131 132—133 171 182
Quantum algebra 143 150
Rados 73 181
| Rank of matrix 27 30 40 80
Rank of matrix, criteria for 92—93
Rank of matrix, of quadratic form 86
Rasch 166
Rational canonical forms, collineatory 45 49
Rational canonical forms, congruent Hermitian 85
Rational canonical forms, congruent Hermitian, skew 88
Rational canonical forms, of correlation 138—139 141 142
Rational canonical forms, of quadratic pencils 116 133—134
Real canonical forms 72 182
Reciprocal bilinear form 162
Reciprocal bilinear form, collineation 40
Reciprocal bilinear form, matrix 4
Reciprocation, polar 153 182
rectangular arrays 9
Rectangular arrays, bilinear form 15
Rectangular arrays, matrix 2
Recurrent determinant 56
Reduced characteristic equation 48
Reduced characteristic equation, function 46—62
Reiss 179
Relative invariant 154
Resolution into symmetric factors 152—153
Resolvent 160 184
Resolvent, partial 163—164 166
Reversal law 4
Richardson, R. G. D. 81 178
Ring 20 21 23 27
Roots, latent 41 44
Roots, of orthogonal polynomials 102 185
Sample quadratic moments 175—176
Scalar matrix 4
Scalar matrix, matrix functions 73 81 149 151 166
Scalar matrix, multiplication 2
Schmidt 95—96 99
schur 81 99
Schwartzian inequality 39
Secondary diagonal 11
Secondary diagonal, unit matrix 151 152
Secular equation 108
Secular equation, elementary divisors 108
Segre characteristic 61 64 70 79 142 147
Self-conjugate triangle 1 182
Self-conjugate triangle, permutation 11
Semi-isolation 8
Sherwood 142
Signature of quadratic form 90 132 142
simplex 40 41 54
Singular collineation 40
Singular collineation, matrix 4
Singular collineation, pencil 114 125—128
Singular collineation, pencil of bilinear forms 129—130
Singular collineation, pencil of quadratic forms 134—135
Skew determinants 99
Skew determinants, latent roots of 101 106
Skew determinants, matrices and forms 33—34 87 98
Skew determinants, symmetric pencils 133
Smith, H. J. S. 9 18 21—23 30 176
Spottiswoode 56
Squares, least 9 173
Standard deviation 173 176
Statistics 173 178
Stickelberger 142
Study 166
Subgroups of equivalent group 32—36
Submatrices 5
Submatrices, partitioned 6
Sylvester 28 30 44 73 76—77 78 81 99 111 137 160 166
Sylvester, interpolation formula of 76—77 81
Symmetrical bilinear form 83
Symmetrical bilinear form, determinant 99
Symmetrical bilinear form, latent toots of 101 106
Symmetrical bilinear form, matrix 32
Symmetrical bilinear form, partitioning 6
Szasz 99
Taber 166
Tchebychef, polynomials 102
Theorem, Cayley — Hamilton 43—44
Theorem, of corresponding matrices 9
Transformations, collineatory, congruent, &c. 35—36
Transformations, elementary 10—13
Transformations, linear 13
Transformations, unimodular 12
Trott, G. R. 142
Turnbull, H. W. 142
Unimodular transformation 12
Unit matrix 2
Unit matrix, auxiliary 62
Unit matrix, secondary 11 151 153
Unitary determinants of 35 36 183
Unitary determinants of, latent roots of 107 108
Unitary matrix 32
Unitary matrix, compounds of 183
Vandermonde 9
Variables, cogredient 37 38
Variables, contragredient 37
Variance, statistical 176
Vector, apolar 121
Vector, binary 119
Vector, chains 43 46 49 54
Vector, dependence of 45 119
Vector, Differentiation 173
Vector, grade of 47 53
Vector, iso tropic 103
Vector, minimal 124
Vector, norm of 38
Vector, normalized 39 97
Vector, point and prime 2
Vector, transposed 2
Vibrations, dynamical 161 171 178
Voss 166
Wedderburn, J. H. M. 56 166 179
Wegner, K. W. 142
Weierstrass 30 80 131—132 166 178
Weierstrass, canonical pencil of quadratics 131—132
Weyr, Ed. 80 81
Whittaker 171 182
Williamson 142 178
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