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Wedderburn J.H.M. — Lectures on Matrices
Wedderburn J.H.M. — Lectures on Matrices

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Название: Lectures on Matrices

Автор: Wedderburn J.H.M.

Аннотация:

This definitive presentation of matrix theory is the work of one of America’s most significant contributors to this area. The first three chapters take matrix theory up to elementary divisors, proceeding to examinations of vector polynomials and singular matric polynomials. A discussion of compound matrices follows, succeeded by considerations of Hermitian, symmetric, and skew matrices, with a number of interesting proofs of properties. Subsequent chapters are devoted to commutative matrices, matrix functions, and the automorphic transformation of a bilinear form. The final chapter offers a masterly handling of linear associative algebras.


Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1934

Количество страниц: 212

Добавлена в каталог: 19.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $y^m=x$      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
1 2
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