Linear Algebra, 2020a

matrix representing, 212–222, 224
nonsingular, 227
null space, 204
nullity, 204
range space, 200
rank, 225
singular, 227
zero, 192
hyperplane, 40
ideal
line, 386
point, 386
identity
function, A-8
matrix, 247
if-then statement, A-2
ill-conditioned problem, 73
image, under a function, A-7
index of nilpotency, 430
induction, 26, A-3
inductive hypothesis, A-3
induction, mathematical, A-3
inductive hypothesis, A-3
inductive step, of induction proof, A-3
inherited operations, 85
inner product, 43
Input-Output Analysis, 67–71
internal direct sum, 148, 183
intersection, of sets, A-6
invariant subspace, 439, 456
inverse, 255, A-8
additive, 84
exists, 256
function, A-8
left, A-8
right, A-8
left, 255, A-8
matrix, 366
right, 255, A-8
two-sided, A-8
inverse function, 255, A-8
inverse image, 201
inversion, 347, A-8
irreducible polynomial, 399
isometry, 319
isomorphism, 173–190
classes characterized by dimension,
184
definition, 175
of a space with itself, 177
Jordan block, 452, 454
Jordan chain, 452
Jordan form, 440–463
definition, 454
represents similarity classes, 454
Jordan string, 452
kernel, of linear map, 204
Kirchhoff’s Laws, 77
Klein, F., 319
Laplace determinant expansion, 363–368
Last Supper, 380
leading
entry, 15
variable, 6
least squares, 295–300
left inverse, A-8
length of a vector, 42
Leontief, W., 67
line, 38
best fit, 296
in projective plane, 385
line at infinity, 386
line of best fit, 295–300
linear combination, 2
Linear Combination Lemma, 57
linear elimination, 3
linear equation, 2
coefficients, 2
constant, 2
homogeneous, 24
inconsistent systems, 295
satisfied by a vector, 17
solution of, 2
Cramer’s rule, 370
Gauss’s Method, 4
Gauss-Jordan, 51
system of, 2
linear extension of a function, 194