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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 |
Addition in a field 6
Addition, vector 17
Adjacency matrix 353
Adjoint matrix 213
Adjoint transformation 339
Affine subset 86
Affine transformation 86
Algebra 33
Algebra, anticommutative 34
Algebra, associative 33
Algebra, Cayley 302
Algebra, commutative 34
Algebra, division 45
Algebra, entire 38
Algebra, exterior 416
Algebra, Jordan 37
Algebra, Lie 35
Algebra, optimization 10
Algebra, quaternion 58
Algebra, tensor 415
Algebra, unital 33
algebraic 65
Algebraic multiplicity 244
Algebraically closed 43
Alphabet 20
angle 325
Annihilate 247
Anti-Hermitian matrix 366
Anticommutative algebra 34
Antitrace 296
Apollonius' identity 323
Arnoldi process 331
Associative algebra 33
Automorphism 101
Automorphism of algebras 101
Automorphism, elementary 102
Automorphism, unitary 369
Axiom of Choice 3
Band matrix 133
Basis 55
Basis, canonical 57 271
Basis, dual 290
Basis, Hamel 61
Bernstein function 94
Bessel's identity 336
Best approximation 395
Bijective 2
Bilinear form 401
Bilinear form, nondegenerate 401
Bilinear transformation 399
Bilinear transformation, symmetric 399
Binet — Cauchy identity 322
Binomial formula 16
block form 123
Bounded 60 307
Bounded support 347
Bra-ket product 121
Brauer's theorem 314
Canonical basis 57 271
Cantor set 61
Cartesian product 2
Cassini oval 314
Cauchy — Schwarz — Bunyakovsky Theorem 304
Cayley algebra 302
Cayley — Hamilton theorem 250
Chain 53
Chain subset 53
Change-of-basis matrix 146
Characteristic 10
Characteristic function 21
Characteristic polynomial 239 268
Characteristic value 229
Characteristic vector 229
Chebyshev polynomial 327
Cholesky decomposition 360
Circulant matrix 156
Co-independent hyperplanes 298
Coefficient 38
Coefficient matrix 171
Coefficient, Fourier 333
Coefficient, leading 38
Coefficient, Taylor 104
Column equivalent 145
Column space 179
Combination, linear 24
Commutative algebra 34
Commuting pair 36
Companion matrix 240
Complement 68
Complement, orthogonal 330
Completely reducible 43
Complex conjugate 8
Complex number 7
Condition number 190
Condition number, spectral 383
Congruent matrices 403
Conjugate transpose 301
Conjugate, complex 8
Continuant 221
Convex subset 365
Coproduct, direct 22
Courant — Fischer minimax theorem 354
Cramer's theorem 215
Cross product 36
Crout's algorithm 153
Cyclic 104
Cyclotomic polynomial 42
Decomposition, Cholesky 360
Decomposition, direct sum 67
Decomposition, LU 153
Decomposition, polar 382
Decomposition, QR 335
Decomposition, singular value 382
Decomposition, spectral 379
Defective eigenvalue 244
Degree of a generalized eigenvector 275
Degree of a polynomial 38
Degree of a polynomial function 41
Derivation 100
Derogatory endomorphism 244
Determinant 205
Determinant function 199
Diagonal matrix 132
Diagonalizable endomorphism 236
Difference set 2
Differential 80
Differential operator 100
DIMENSION 63
Dirac functional 289
Direct coproduct 22
Direct product 19
Direct sum 66
Direct sum decomposition 67
Discrete cosine transform 137
Discrete Fourier Transform 136 308
Disjoint subspaces 23
Distance 315
distribution 286
Division algebra 45
Division algorithm 40
Domain 2
Domain, integral 10
Dot product 300
Dot product, weighted 301
Dual basis 290
Dual space 285
Dual space, weak 290
Dyadic product 130
Eigenspace 231 233
Eigenspace, generalized 276
| Eigenvalue 229 232
Eigenvalue, defective 244
Eigenvalue, semisimple 244
Eigenvalue, simple 244
Eigenvector 229 232
Eigenvector, generalized 275
Eisenstein's criterion 42
Elementary automorphism 102
Elementary matrix 137
Elementary operation 143
Endomorphism 99
Endomorphism, bounded 112
Endomorphism, derogatory 244
Endomorphism, diagonalizable 236
Endomorphism, nilpotent 272
Endomorphism, normal 375
Endomorphism, orthogonally diagonalizable 352
Endomorphism, positive definite 356
Endomorphism, selfadjoint 349
Entangled tensors 410
Entire 38
EPIC 2
Epimorphism 85
Equal functions 2
Equivalence relation 106
Equivalent matrices 145
Euclidean norm 305
Euclidean subfield 299
Evaluation functional 291
Even function 69
Even permutation 203
Exchange property 26
Extended coefficient matrix 171
Exterior algebra 416
Exterior power 416
Exterior product 121
Exterior square 416
Factor space 98
Fan 168
Fast Fourier Transform 136
Fibonacci sequence 269
Field 6
Field of algebraic numbers 65
Field, algebraically closed 43
Field, formally-real 300
Field, Galois 9
Field, orderable 16
Finite dimensional 63
Finitely generated 26
Fixed point 231
Fixed space 231
Form, bilinear 401
Form, Lorentz 408
Form, quadratic 407
Formal differentiation 104
Formally real field 300
Fourier coefficient 333
Fredholm alternative 293
Frobenius norm 311
Full pivoting 152
Function 2
Function, characteristic 21
Function, determinant 199
Function, even 69
Function, inverse 2
Function, odd 69
Function, periodic 62
Function, piecewise constant 30
Function, spline 48
Functional, Dirac 289
Functional, evaluation 291
Functional, linear 285
Functional, zero 285
Fundamental theorem of algebra 43
Galois field 9
Gauss — Jordan method 175
Gauss — Seidel iteration method 186
Gaussian elimination 175
General Lie algebra 131
General quadratic equation 410
Generalized eigenspace 276
Generalized eigenvector 275
Generating set 25
Geometric multiplicity 244
Gershgorin bound 312
Gershgorin's theorem 312
Givens rotation matrix 370
GMRES algorithm 331
Golden ratio 269
Google matrix 254
Gram matrix 303
Gram — Schmidt process 328
Gram — Schmidt Theorem 328
Graph 81
Grassmann's Theorem 69
Greville's method 392
Group of automorphisms 107
Guttman's Theorem 138
Haar wavelet 332
Hadamard inequality 329
Hadamard matrix 207
Hadamard product 157
Hamel basis 61
Hamming norm 315
Hankel matrix 219
Hausdorff maximum principle 60
Hermitian matrix 351
Hermitian transpose 301
Hibert subset 332
Hilbert matrix 144
Hilbert — Schmidt norm 311
Homogeneous system of linear equations 170
Homomorphism 79
Homomorphism of algebras 79
Homomorphism of unital algebras 79
Householder matrix 373
Hyperplane 292
Ill-conditioned 189
Image 85
Imaginary part 7
Improper subspace 22
Independent subspaces 67
Indeterminate 38
Index of nilpotence 272
Induced norm 310
Infinite dimensional 63
Inner product 299
Inner product space 300
Integral domain 10
Interior product 121
Interpolation problem 169
Intersection 2
Invariant subspace 103
Inverse function 2
inversion 202
Involution 341
Irreducible 41
Isometry 362
Isomorphic vector spaces 87
Isomorphism 85
Isomorphism of algebras 85
Isomorphism of unital algebras 85
Iteration method, Gauss — Seidel 186
Iteration method, Jacobi 186
Jacobi identity 36
Jacobi iteration method 186
Jacobi overrelaxation method 188
Jacobi polynomial 327
JOR 188
Jordan algebra 37
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