Page 536 - Advanced Linear Algebra

520 Index

orthogonal complement, 212, 265 projection theorem, 220, 334
orthogonal direct sum, 212, 269 projection, 73
orthogonal geometry, 260 projective dimension, 438
orthogonal group, 271 projective geometry, 438
orthogonal resolution of the identity, 232 projective line, 438
orthogonal set, 212 projective plane, 438
orthogonal similarity classes, 242 projective point, 438
orthogonal spectral resolution, 237 proper subspace, 37
orthogonal transformation, 271 properly divides, 27
orthogonal, 75, 212, 231, 238, 265 pseudobasis, 472
orthogonality conditions, 480 pure in, 161
orthogonally diagonalizable, 233
orthogonally equivalent, 242 q-binomial coefficients, 506
orthogonally similar, 242 quadratic form, 239, 264
orthonormal basis, 218 quaternions, 463
orthonormal set, 212 quotient algebra, 455
quotient field, 24
parallel, 427 quotient module, 118
parallelogram law, 208, 325 quotient ring, 22
parity, 391 quotient space, 87, 89
Parseval's identity, 221, 346
partial order, 10 radical, 266
partially ordered set, 10 range, 6
partition, 7 rank, 53, 61, 129, 369
permutation, 391 rank plus nullity theorem, 63
Pincherle derivative, 503 rational canonical form, 176–179
plane, 427 real operator, 59
point, 427 real part, 54
polar decomposition, 253 real vector space, 36
polarization identities, 209 real version, 53
posets, 10 recurrence formula, 501
positive definite, 205, 250, 301 reduce, 169
positive square root, 251 reduced row echelon form, 3, 4
power of the continuum, 16 reflection, 244, 292
power set, 13 reflexivity, 7, 10
primary, 147 relatively prime, 5, 27
primary cyclic decomposition theorem, 153, 168 representation, 457
primary decomposition theorem, 147 resolution of the identity, 76
primary decomposition, 147, 168 restriction, 6
prime subfield, 97 retract, 122
prime, 26 retraction map, 122
primitive, 465 Riesz map, 222
principal ideal domain, 24 Riesz representation theorem, 222, 268, 351
principal ideal, 24 Riesz vector, 222
product, 15 right inverse, 122, 470
projection modulo, 89 right singular vectors, 445