Linear Algebra, 2020a

equivalence, A-11
representative, A-11
closure, 100
of null space, 427
of range space, 427
codomain, A-7
cofactor, 364
column, 15
rank, 137
full, 143
space, 137
vector, 16
combining rows, 5
complement, A-6
complementary subspaces, 148
orthogonal, 288
complete equation, 165
complex numbers, 400
vector space over, 95, 398
component of a vector, 16
composition, A-7
self, 424
computer algebra systems, 65–66
computer graphics, 392–396
concatenation of sequences, 146
conditioning number, 75
congruent plane figures, 319
constant polynomial, 398
contradiction, A-4
contrapositive, A-2
convex set, 198
coordinates
homogeneous, 383, 392
with respect to a basis, 124
correspondence, 175, A-9
coset, 210
Coupled Oscillators, 482–486
Cramer’s rule, 369–371
cross product, 330
crystals, 155–158
unit cell, 156
da Vinci, Leonardo, 380
dangling link, 471
degree of a polynomial, 398
Desargue’s Theorem, 387
determinant, 326, 331–354
Cramer’s rule, 370
definition, 332
exists, 343, 349
Laplace expansion, 365
minor, 364
permutation expansion, 342, 346, 372
using cofactors, 364
diagonal matrix, 230, 248
diagonalizable, 408–412
diamond, 157
dilation, 177, 303
representing, 221
dimension, 131
dimensional
constant, 165
formula, 165
direct map, 323
direct sum, 144–152
definition, 148
external, 183
internal, 183
of two subspaces, 148
direction vector, 39
distance-preserving map, 319
division theorem, 398
domain, A-7
dot product, 43
double precision, 74
dual space, 210
Duality Principle, of projective geometry,
386
echelon form, 6
free variable, 13
leading entry, 15
leading variable, 6
matrix, 15
reduced, 51
eigenspace, 417
eigenvalue, eigenvector
of a matrix, 413
of a transformation, 412
element, A-5
elementary matrix, 250
elementary reduction matrix, 250, 302