Page 537 - Advanced Linear Algebra

Index 521

right zero divisor, 460 standard basis, 47, 62, 131
right-invertible, 470 standard inner product, 206
ring, 18 standard topology, 79
ring homomorphism, 19 standard vector, 47
ring with identity, 19 Stirling numbers of the second kind, 502
roots of unity, 464 strictly diagonally dominant, 203
rotation, 292 strictly positive orthant, 411
row equivalent, 4 strictly positive, 225, 411
row rank, 52 strictly separated, 417
row space, 52 strongly positive orthant, 225, 411
strongly positive, 56, 225, 411
scalar multiplication, 31, 35, 451 strongly separated, 417
scalars, 2, 35, 109 structure constants, 453
Schröder, 13 structure theorem for normal matrices, 247
Schur's theorem, 192, 195 structure theorem for normal operators, 245
second isomorphism theorem, 93, 119 subalgebra, 454
self-adjoint, 238 subfield, 57
separable, 308 subgroup, 18
sesquilinear, 206 submatrix, 2
Sheffer for, 481 submodule, 111
Sheffer identity, 486 subring, 19
Sheffer operator, 491, 498 subspace spanned, 44
Sheffer sequence, 481 subspace, 37, 260, 304
Sheffer shift, 491 sup metric, 302
sign, 391 support, 6, 41
signature, 288 surjection, 6
similar, 9, 70, 71 surjective, 6
similarity classes, 70, 71 Sylvester's law of inertia, 287
simple, 138, 455 symmetric, 2, 238, 259, 390, 395
simultaneously diagonalizable, 202 symmetric group, 391
singular, 266 symmetric tensor algebra, 398
singular values, 444, 445 symmetric tensor space, 395, 400
singular-value decomposition, 445 symmetrization map, 402
skew self-adjoint, 238 symplectic basis, 273
skew-Hermitian, 238 symplectic geometry, 260
skew-symmetric, 2, 238, 259, 390 symplectic group, 271
smallest, 10 symplectic transformation, 271
span, 45, 112 symplectic transvection, 280
spectral mapping theorem, 187, 461
spectral theorem for normal operators, 236, 237 tensor algebra, 390
spectral resolution, 197 tensor map, 362, 383
spectrum, 186, 461 tensor product, 362, 383, 408
sphere, 304 tensors of type, 386
split, 5 tensors, 362
square summable, 207 theorem of the alternative, 413
square summable functions, 347 third isomorphism theorem, 94, 119