Page 535 - Advanced Linear Algebra

Index 519

linear code, 38 Moore-Penrose pseudoinverse, 446
linear combination, 36, 112 MP inverse, 447
linear function, 382 multilinear, 382
linear functional, 59, 94 multilinear form, 382
linear hyperplane, 416 multiplicity, 1
linear least squares, 448 multiset, 1
linear operator, 59
linear transformation, 59 natural map, 100
linearity, 340 natural projection, 89
linearity in the first coordinate, 205 natural topology, 80, 82
linearly dependent, 45, 114 negative, 17
linearly independent, 45, 114 net definition, 339
linearly ordered set, 11 nilpotent, 198, 200
lower bound, 11 Noetherian, 133
lower factorial numbers, 471 nondegenerate, 266
lower factorial polynomials, 488 nonderogatory, 171
lower triangular, 4 nonisotropic, 265
nonnegative orthant, 225, 411
main diagonal, 2 nonnegative, 225, 411
matrix, 64 nonsingular, 266
matrix of, 66 nonsingular completion, 273
matrix of the form, 261 nonsingular extension theorem, 274
maximal element, 10 nontrivial, 36
maximal ideal, 23 norm, 208, 209, 303, 349
maximal orthonormal set, 218 normal equations, 449
maximum, 10 normal, 234
measuring family, 357 normalizing, 213
measuring functions, 357 normed linear space, 209, 224
mediating morphism map, 367 null, 265
mediating morphism, 357, 362, 383 nullity, 61
meet, 40
metric, 210, 301 odd permutation, 391
metric space, 210, 301 one-sided inverses, 122, 470
metric vector space, 260 one-to-one, 6
mimimum, 10 onto, 6
minimal element, 11 open ball, 304
minimal polynomial, 165, 166, 459 open half-spaces, 417
Minkowski space, 260 open neighborhood, 304
Minkowski's inequality, 37, 303 open rectangles, 79
mixed tensors, 386 open sets, 305
modular law, 56 operator adjoint, 104
module, 109, 133, 167 operator characterization, 484
modulo, 22, 87, 118 order, 18, 101, 139, 471
monic, 5 order ideals, 115
monomorphism, 59, 117 ordered basis, 51
Moore-Penrose generalized inverse, 446 order-reversing, 102