Linear Algebra

characteristic polynomial, 360
composed with itself, 365
diagonalizable, 354
eigenspace, 361
eigenvalue, eigenvector, 357
Jordan form for, 392
minimal polynomial, 380
nilpotent, 370
canonical representative, 374
projection, 385
size change, 321
transpose, 19, 126
determinant, 309, 317
interaction with sum and scalar
multiplication, 213
Triangle Inequality, 40
triangular matrix, 229
Triangularization, 204
trivial space, 84, 114
turning map, 164
unit matrix, 222
Vandermonde matrix, 311
vanishing point, 337
vector, 15, 33
angle, 42
canonical position, 33
column, 15
component, 15
cross product, 298
direction, 35
dot product, 39
free, 33
homogeneous coordinate, 340
length, 39
orthogonal, 42
representation of, 116, 238
row, 15
satisfies an equation, 15
scalar multiple, 15, 34, 80
sum, 15, 34, 35, 80
unit, 43
zero, 22, 80
vector space, 80–101
basis, 113
closure, 80
complex scalars, 91
definition, 80
dimension, 121
dual, 193
finite dimensional, 119
homomorphism, 176
isomorphism, 161
map, 176
over complex numbers, 347
subspace, 91
trivial, 84, 114
volume, 321
voting paradox, 147
majority cycle, 147
rational preference order, 147
voting paradoxes, 147–151
spin, 149
well-defined, A-8
Wheatstone bridge, 75
zero
divisor, 220
zero divison, 237
zero divisor, 220
zero homomorphism, 177
zero vector, 22, 80