|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Mirsky L. — An introduction to linear algebra |
|
|
|
| Предметный указатель |
Ostrowski’s inequality 212-13
Partitioned matrices 100-6
Periodic matrices 298
Permutation matrices 271
permutations 256-9
Permutations, groups of 257-8 271-2
Polar representation 425
Polarized, form 362
Polarized, form, operator 361
Polynomial, characteristic 195 197-208
Polynomial, identity and formal equality 24
Polynomial, in a matrix 97-99 201-8 342-3
Polynomial, minimum 203-4 207-8 297-8
Polynomial, monic 203
Positive definite forms 394 398-404
Power series of matrices 332-43
Premultiplication and postmultiplication 81
Principal axes, reduction of quadrics to 364-7
Principal, minor 197
Principal, minor, vector 237
Projection 130
Projective, classification of quadrics 380-1
Projective, classification of quadrics, group 263
Quadratic form(s), as product of two linear forms 374-6
Quadratic form(s), canonical forms 378
Quadratic form(s), definite and indefinite 394
Quadratic form(s), definition 357
Quadratic form(s), determinant 359
Quadratic form(s), diagonal forms 362
Quadratic form(s), equivalence 376-9
Quadratic form(s), general reduction 369-74
Quadratic form(s), law of inertia 377
Quadratic form(s), orthogonal reduction 362-3
Quadratic form(s), positive definite forms 394 398-404
Quadratic form(s), rank 360
Quadratic form(s), simultaneous reduction 408-15
Quadratic form(s), singular and non-singular 359
Quadratic form(s), unit’ forms 362
Quadratic operators 357-9 361-2
Quadrics, classification 380-5
Quadrics, classification, reduction to principal axes 364-7
Quaternions 265
Rank, of a bilinear form 356
Rank, of a linear transformation 277
Rank, of a matrix 136-40
Rank, of a quadratic form 360
Rank, properties 158-63 169
Rank, rank theorem 139
Rank, rank-multiplicity theorem 214
Rational, functions of matrices 99 100 201-2 204-5 335
Rational, functions of matrices, reduction 185
Reduction, f hermitian forms 387
Reduction, f matrices to normal form 173-6
Reduction, f quadratic forms 369-74
Reduction, f quadrics to principal axes 364-7
Reduction, Lagrange’s method 371-4
Reduction, of bilinear forms 368-9
Reduction, orthogonal reduction of quadratic forms 362-3
Reduction, orthogonal reduction of symmetric matrices 302-4
Reduction, rational 185
Reduction, simultaneous reduction of two hermitian forms 415
Reduction, simultaneous reduction of two quadratic forms 408-15
Redundant equations 131
Reference field 40
Regular characteristic roots 294
Replacement theorem of Steinitz 53 (footnote)
Representation, of bilinear operators by bilinear forms 354
Representation, of groups by matrices 267-72
Representation, of linear manifolds by vector spaces 60
Representation, of linear operators by matrices 114-22
Representation, of quadratic forms as sums of squares 370-1
Representation, of quadratic operators by quadratic forms 358
Representation, of rotations by orthogonal matrices 233-43 246-7
Representation, of rotations by skew- symmetric matrices 243-5
Representation, polar 425
Rigid motion 246-7
Rotation, axis 240
Rotation, in space 236-47
Rotation, in the plane 233-6
Rotation, infinitesimal 249
Rotation, representation by orthogonal matrices 233-43 246-7
Rotation, representation by skew- symmetric matrices 243-5
Rotation, rotation group 263
Row, matrices and vectors 77
| Row, matrices and vectors, rank 137
Scalar, matrix 76
Scalar, product see Inner product
Scalars 40
Schmidt’s orthogonalization process 67-68
Schur and Toeplitz, theorem on normal matrices 305
Schur, inequality for characteristic roots 309-11
Schur, inequality for positive definite matrices 422
Schur, theorem on triangular canonical forms 307
Secular equation 196
Semi-definite forms 394 405-7
Separation 63
Signature 378-80 387-8 398
Signum 3
Similar matrices 119
Similarity, group 266
Similarity, orthogonal and unitary 266
Similarity, transformation 119
Simultaneous, equations see Linear equations
Simultaneous, reduction of two hermitian forms 415
Simultaneous, reduction of two quadratic forms 408-15
Simultaneous, similarity transformations 316 22
Singular and non-singular matrices 87
Singular matrices, groups of 272-6
Skew-Hermitian matrices 209 232
Skew-symmetric matrices 208 227 243-5
Small vibrations 415-16
Square matrices 75
Steinitz’s replacement theorem 53 (footnote)
Sub-group 254
Sub-manifold 45
Sub-matrix 136
Sub-space 45
Sylvester, interpolation formula 221
Sylvester, law of inertia 377
Sylvester, law of nullity 162
Symmotnc, bilinear operators 361
Symmotnc, group 257
Symmotnc, matrix 183
toeplitz see Schur
Total vector space 42
Trace 198
Transformations, congruence 182-5 266 358-60
Transformations, definition 113
Transformations, equivalence 177
Transformations, linear 114-22 277 356 360
Transformations, similarity 119
Transposition, of arrangements 3 258
Transposition, of arrangements of matrices 76 97
Triangle inequality 64
Triangular, canonical forms 306-9
Triangular, matrices 76
Unit, matrix 75
Unit, quadratic form 362
Unit, vector 64
Unitary, group 263
Unitary, matrices 229-32
Unitary, reduction of hermitian forms 387
Unitary, similarity 266
Value classes, definition 394
Value classes, determinantal criteria 400-7
Vandermonde determinant 17-18
Vector space, basis theorem 52
Vector space, definition 42
Vector space, generators 43
Vector space, spanned by given vectors 43
Vector(s), addition 41
Vector(s), characteristic 214
Vector(s), column type and row type 77
Vector(s), definition 40
Vector(s), length 63
Vector(s), linear combination 42
Vector(s), linear dependence 48 152-3
Vector(s), multiplication by scalars 40
Vector(s), norm 63
Vector(s), normalization 64
Vector(s), orthogonal and orthonormal 65
Vector(s), principal 237
Vector(s), zero 40
Weierstrass’s theorem on simultaneous reduction of two forms 410
Weyr’s theorem on matrix power series 332
Zero, divisors of 95-96 153-4
Zero, element of a linear manifold 45
Zero, matrix 75
Zero, vector 40
|
|
|
| Реклама |
|
|
|
|
|
О проекте