Page 533 - Advanced Linear Algebra
P. 533
Index 517
degenerate, 266 essentially unique, 45
degree, 5 Euclidean metric, 302
deleted absolute row sum, 203 Euclidean space, 206
delta functional, 475 evaluation at, 96, 100
delta operator, 478 evaluation functional, 474, 476
delta series, 472 even permutation, 391
dense, 308 even weight subspace, 38
derivation, 499 exponential polynomials, 502
descendants, 13 exponential, 482
determinant, 292, 405 extension by, 103
diagonal, 4 extension, 6, 273
diagonalizable, 196 exterior algebra, 398
diagonally dominant, 203 exterior product, 393
diameter, 321 exterior product space, 395, 400
dimension, 50, 427 external direct sum, 40, 41, 119
direct product, 41, 408
direct sum, 41, 73, 119 factored through, 355, 357
direct summand, 42, 120 factorization, 217
discrete metric, 302 faithful, 457
discriminant, 263 Farkas's lemma, 423
distance, 209, 322 field of quotients, 24
divides, 5, 26 field, 19, 29
division algebra, 462 finite support, 41
division algorithm, 5 finite, 1, 12, 18
domain, 6 finite-dimensional, 50, 451
dot product, 206 finitely generated, 113
double, 100 first isomorphism theorem, 92, 118, 469
dual basis, 96 flat representative, 427
dual space, 59, 100 flat, 427
form, 299, 382
eigenspace, 186 forward difference functional, 477
eigenvalue, 185, 186, 461 forward difference operator, 479
eigenvector, 186 Fourier coefficient, 219
elementary divisor basis, 169 Fourier expansion, 219, 338, 345
elementary divisor form, 176 free, 116
elementary divisor version, 177 Frobenius norm, 450, 466
elementary divisors, 155, 167, 168 functional calculus, 248
elementary divisors and dimensions, 168 functional, 94
elementary matrix, 3
elementary symmetric functions, 189 Gaussian coefficients, 57, 506
embedding, 59, 117 generating function, 482, 483
endomorphism, 59, 117 geometric multiplicity, 189
epimorphism, 59, 117 Geršgorin region, 203
equivalence class, 7 Geršgorin row disk, 203
equivalence relation, 7 Geršgorin row region, 203
equivalent, 9, 69 graded algebra, 392
