Linear Algebra

educed echelon form, 46
reflection, 289
glide, 289
reflection (or flip) about a line, 164
relation, A-9
equivalence, A-10
relationship
linear, 103
representation
of a matrix, 196
of a vector, 116
representative, A-11
canonical, A-12
for row equivalence classes, 57
of matrix equivalence classes, 245
of similarity classes, 392
rescaling rows, 4
restriction, A-9
rigid motion, 286
rotation, 274, 288
rotation (or turning), 164
represented, 199
row, 13
rank, 124
vector, 15
row equivalence, 50
row rank
full, 131
row space, 124
scalar, 80
scalar multiple
matrix, 212
vector, 15, 34, 80
scalar product, 39
Schwartz Inequality, 41
SciLab, 61
self composition
of maps, 365
sense, 321
sequence, A-8
concatenation, 134
sets, A-6
dependent, independent, 103
empty, 105
mutual inclusion, A-7
proper subset, A-7
span of, 95
subset, A-7
sgn
seesignum, 314
signum, 314
similar, 298, 324
canonical form, 392
similar matrices, 351
similarity, 351–364
similarity transformation, 364
singular
matrix, 27
size, 319, 321
skew, 276
skew-symmetric, 311
span, 95
of a singleton, 99
spin, 149
square root, 398
stable populations, 403–404
standard basis, 114
Statics problem, 5
string, 371
basis, 371
of basis vectors, 369
structure
preservation, 176
submatrix, 303
subspace, 91–101
closed, 93
complementary, 136
definition, 91
direct sum, 135
improper, 92
independence, 135
invariant, 389
orthocomplement, 139
proper, 92
sum, 132
sum
of matrices, 212
of subspaces, 132
vector, 15, 34, 80
summation notation
for permutation expansion, 308
swapping rows, 4
symmetric matrix, 118, 139, 213, 220
system of linear equations, 2
Gauss’ method, 2
solving, 2
trace, 213, 229, 397
transformation