Linear Algebra, 2020a

trace, 235, 253, 309, 462
transition, 314
transpose, 22, 138, 235
triangular, 222, 253, 368
tridiagonal, 466
unit, 245
Vandermonde, 345
zero, 234
matrix equivalence, 267–274
canonical form, 271
definition, 270
member, A-5
method of powers, 464–467
minimal polynomial, 244, 441
minor, of a matrix, 364
morphism, 175
multilinear, 338
multiplication
matrix-matrix, 237
matrix-vector, 215
multiplicity
algebraic, 418
geometric, 418
multiplicity, of a root, 399
multiset, 113, A-6
mutual inclusion, A-5
natural representative, A-11
networks, 76–81
Kirchhoff’s Laws, 77
nilpotency, index of, 430
nilpotent, 428–439
canonical form for, 435
definition, 430
matrix, 430
transformation, 430
nonsingular, 227, 256
homomorphism, 227
matrix, 30
normalize, vector, 43, 283
null space, 204
closure of, 427
generalized, 427
nullity, 204
odd function, 105, 150
one-to-one function, A-8
onto function, A-8
opposite map, 323
ordered pair, A-7
orientation, 357, 361
orientation preserving map, 323
orientation reversing map, 323
orthogonal, 46
basis, 281
complement, 288
mutually, 280
projection, 288
orthogonal matrix, 321
orthogonalization, 282
orthonormal basis, 283
orthonormal matrix, 319–324
page ranking, 470–473
pair, ordered, A-7
parallelepiped, 355
parallelogram rule, 38
parameter, 14
parametrized, 14
partial pivoting, 74
partition, A-9–A-11
into isomorphism classes, 184
matrix equivalence classes, 270, 272
row equivalence classes, 53
permutation, 341
inversions, 347
matrix, 248
signum, 349
permutation expansion, 342, 346, 372
permutation matrix, 341
perp, of a subspace, 288
perpendicular, 46
perspective, triangles, 387
physical dimension, 165
pivoting, 51
full, 74
partial
scaled, 75
plane figure, 319
congruence, 319
point
at infinity, 386