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| Golan J.S. — The Linear Algebra a Beginning Graduate Student Ought to Know (Texts in the Mathematical Sciences) |
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| Предметный указатель |
Jordan canonical form 275 278
Jordan identity 37
Jordan product 37
Karatsuba's algorithm 39
Kernel 84
Ket-bra product 121
Kovarik algorithm 393
Kronecker product 413
Krylov algorithm 271
Krylov subspace 267
Lagrange identity 306
Lagrange interpolation polynomial 146
Lanczos algorithm 271
Leading coefficient 38
Leading entry 174
Least squares method 395
Legendre polynomial 326
Lie algebra 35
Lie algebra, general 131
Lie algebra, special 286
Lie product 36
Lightcone inequality 409
linear combination 24
Linear functional 285
Linear transformation 79
Linear transformation, adjoint of 339
Linearly dependent 49
Linearly dependent, locally 82
Linearly independent 49
Linearly recurrent sequence 268
LIST 1
Locally linearly dependent 82
Loewner partial order 357
Lorentz form 408
Lower-triangular matrix 134
LU-Decomposition 153
Magic matrix 259
Markov matrix 135
Matrices, column-equivalent 145
Matrices, congruent 403
Matrices, equivalent 145
Matrices, row-equivalent 145
Matrices, similar 241
Matrices, unitarily similar 370
Matrix 20
Matrix in block form 123
Matrix in reduced row echelon form 174
Matrix in row echelon form 173
Matrix, adjacency 353
Matrix, adjoint 213
Matrix, anti-Hermitian 366
Matrix, band 133
Matrix, change-of-basis 146
Matrix, circulant 156
Matrix, coefficient 171
Matrix, companion 240
Matrix, determinant of 205
Matrix, diagonal 132
Matrix, elementary 137
Matrix, extended coefficient 171
Matrix, Givens rotation 370
Matrix, Google 254
Matrix, Gram 303
Matrix, Hadamard 207
Matrix, Hankel 219
Matrix, hermitian 351
Matrix, Hilbert 144
Matrix, Householder 373
Matrix, lower-triangular 134
Matrix, magic 259
Matrix, Markov 135
Matrix, Nievergelt's 144
Matrix, nonsingular 135
Matrix, normal 384
Matrix, orthogonal 372
Matrix, permutation 142
Matrix, quasidefinite 366
Matrix, scalar 132
Matrix, singular 135
Matrix, skew-symmetric 134
Matrix, sparse 187
Matrix, special orthogonal 375
Matrix, stochastic 135
Matrix, symmetric 134
Matrix, symmetric Toeplitz 183
Matrix, transpose 85
Matrix, tridiagonal 133
Matrix, unitary 370
Matrix, upper Hessenberg 419
Matrix, upper-triangular 133
Matrix, Vandermonde 147
Matrix, zero 21
Maximal 53
Maximal subspace 292
Minimal 53
Minimal polynomial 248 268
Minkowski's inequality 307
Minor 209
Modular law 28
Moebius function 42
Monic function 2
Monic polynomial 38
Monomorphism 85
Moore — Penrose pseudoinverse 389
Multiplication in a field 6
Multiplication table 58
Multiplication, scalar 17
Multiplicity, algebraic 244
Multiplicity, geometric 244
Mutually orthogonal 326
Nievergelt's matrix 144
Nilpotent 272
Nondegenerate bilinear form 401
Nonhomogeneous system of linear equations 170
Nonsingular matrix 135
Nontrivial subspace 22
Norm 305 309
Norm, Euclidean 305
Norm, Frobenius 311
Norm, Hamming 315
Norm, Hilbert — Schmidt 311
Norm, induced 310
Norm, spectral 311
Normal endomorphism 375
Normal matrix 384
Normal vector 305
Normed space 309
Nullity 89
Number, complex 7
Number, rational 5
Number, real 5
Numerical range 409
Odd function 69
Odd permutation 203
Operation, elementary 143
Opposite transformation 399
Optimization algebra 10
Order able field 16
Order of recurrence 268
Orthogonal 326
Orthogonal complement 330
Orthogonal complement, right 403
Orthogonal matrix 372
Orthogonal projection 330
Orthogonality with respect to a bilinear form 403
Orthogonally diagonalizable 352
Orthonormal 331
Pade approximant 216
Pairwise disjoint 24
Parallelogram law 307
| Parity 401
Parseval's identity 336
Partial order 53
Partial order, Loewner 357
Partial pivoting 152
Partially-ordered set 53
Periodic function 62
Permutation 2
Permutation matrix 142
Permutation, even 203
Permutation, odd 203
Pfaffian 206
Piecewise constant 30
Pivot 152
Pivoting, full 152
Pivoting, partial 152
Poincare — Birkhoff — Witt theorem 36
Polar decomposition 382
Polynomial 38
Polynomial function 40
Polynomial in several indeterminates 44
Polynomial, characteristic 239 268
Polynomial, Chebyshev 327
Polynomial, completely reducible 43
Polynomial, cyclotomic 42
Polynomial, irreducible 41
Polynomial, Jacobi 327
Polynomial, Lagrange interpolation 146
Polynomial, Legendre 326
Polynomial, minimal 248 268
Polynomial, monic 38
Polynomial, reducible 41
Polynomial, zero 38
Positive definite 356
Power, exterior 416
Pre-Banach space 309
Pre-Hilbert space 300
Primitive root of unity 136
Process, Arnoldi 331
Process, Gram — Schmidt 328
Product, bra-ket 121
Product, cartesian 2
Product, cross 36
Product, direct 19
Product, dot 300
Product, dyadic 130
Product, exterior 121
Product, Hadamard 157
Product, inner 299
Product, interior 121
Product, Jordan 37
Product, ket-bra 121
Product, Kronecker 413
Product, Lie 36
Product, scalar triple 306
Product, Schur 157
Product, tensor 411
Product, Vector triple 306
Projection 104
Projection onto an affine set 342
Projection, orthogonal 330
Proper subspace 22
Pseudoinverse, Moore — Penrose 389
QR-decomposition 335
Quadratic form 407
Quadratic surface 410
Quasidefinite matrix 366
Quaternion, algebra 58
Quaternion, real 58
RANGE 2
Range, numerical 409
Rank 89 179 403
Rational Decomposition Theorem 274
Rational number 5
Rayleigh quotient, function 354
Rayleigh quotient, iteration scheme 355
Real euclidean 299
Real number 5
Real part 7
Real quaternion 58
Reduced row echelon form 174
Reducible 41
Relation, equivalence 106
Relation, partial order 53
Relaxation method 188
Restriction 2
Riesz representation theorem 338
Right orthogonal complement 403
Row echelon form 173
Row equivalent 145
Row space 179
scalar 18
Scalar matrix 132
Scalar multiplication 17
Scalar triple product 306
Schur product 157
Schur's theorem 371
Selfadjoint 349
Semifield 10
Semisimple eigenvalue 244
SEQUENCE 2
Sequence, Fibonacci 269
Sequence, linearly recurrent 268
Set, difference 2
Set, generating 25
Set, partially-ordered 53
Set, spanning 25
Sherman — Morrison — Woodbury theorem 138
Signum 203
Similar matrices 241
Simple eigenvalue 244
Simple tensors 410
Singular matrix 135
Singular value 383
Singular Value Decomposition Theorem 382
Skew symmetric matrix 134
Solution set 171
Solution space 171
SOR 188
Space, dual 285
Space, inner product 300
Space, normed 309
Space, pre-Banach 309
Space, pre-Hilbert 300
Space, solution 171
Spanning set 25
Sparse matrix 187
Special lie algebra 286
Special orthogonal matrix 375
Spectral condition number 383
Spectral decomposition theorem 379
Spectral norm 311
Spectral radius 233
Spectrum 229
Spline Function 48
Steinitz Replacement Property 52
Stochastic matrix 135
Strassen — Winograd algorithm 150
Subalgebra 35
Subalgebra, unital 35
Subfield 7
Subfield, euclidean 299
Subfield, real euclidean 299
Subset, affine 86
Subset, bounded 60
Subset, chain 53
Subset, convex 365
Subset, Hilbert 332
Subset, orthonormal 331
Subset, underlying 2
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