Page 534 - Advanced Linear Algebra
P. 534
518 Index
Gram-Schmidt augmentation, 213 invariant factor form, 178
Gram-Schmidt orthogonalization process, 214 invariant factor version, 179
greatest common divisor, 5 invariant factors, 157, 167, 168
greatest lower bound, 11 invariant factor decomposition theorem, 157
group algebra, 453 invariant ideals, 157
group, 17 invariant under, 73
inverses, 17
Hamel basis, 218 invertible functional, 475
Hamming distance function, 321 involution, 199
Hermite polynomials, 224, 489 irreducible, 5, 26, 83
Hermitian, 238 isometric isomorphism, 211, 326
Hilbert basis theorem, 136 isometric, 271, 316
Hilbert basis, 218, 335 isometrically isomorphic, 211, 326
Hilbert dimension, 347 isometry, 211, 271, 315, 326
Hilbert space adjoint, 230 isomorphic, 59, 62, 117
Hilbert space, 315, 327 isotropic, 265
Hölder's inequality, 303
homogeneous, 392 join, 40
homomorphism, 59, 117 Jordan basis, 191
Householder transformation, 244 Jordan block, 191
hyperbolic basis, 273 Jordan canonical form, 191
hyperbolic extension, 274
hyperbolic pair, 272 kernel, 61
hyperbolic plane, 272 Kronecker delta function, 96
hyperbolic space, 272 Kronecker product, 408
hyperplane, 416, 427
Lagrange interpolation formula, 248
ideal generated by, 21, 455 Laguerre polynomials, 490
ideal, 20, 455 largest, 10
idempotent, 74, 125 lattice, 39, 40
identity, 17 leading coefficient, 5
image, 6, 61 leading entry, 3
imaginary part, 54 least, 10
indecomposable, 158 least squares solution, 448
index of nilpotence, 200 least upper bound, 11
induced, 305 left inverse, 122, 470
inertia, 288 left regular matrix representation, 457
infinite, 13 left regular representation, 457
infinite-dimensional, 50 left singular vectors, 445
injection, 6, 117 left zero divisor, 460
inner product, 205, 260 left-invertible, 470
inner product space, 205, 260 Legendre polynomials, 215
integral domain, 23 length, 208
invariant, 8, 73, 83, 165 limit, 306
invariant factor basis, 179 limit point, 306
invariant factor decomposition, 157 line, 427, 429
