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Turnbull H.W. — An Introduction to the Theory of Canonical Matrices
Turnbull H.W. — An Introduction to the Theory of Canonical Matrices



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Название: An Introduction to the Theory of Canonical Matrices

Автор: Turnbull H.W.

Аннотация:

Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory’s principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1952

Количество страниц: 192

Добавлена в каталог: 19.11.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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