Linear Algebra, 2020a

elementary reduction operations, 5
rescaling, 5
row combination, 5
swapping, 5
by matrix multiplication, 250
elementary row operations, 5
by matrix multiplication, 250
elimination, Gaussian, 3
empty set, A-5
entry, matrix, 15
equivalence, A-9
class, A-11
canonical representative, A-11
relation, A-9
representative, A-11
equivalence relation, A-9
isomorphism, 184
matrix equivalence, 270
matrix similarity, 404
row equivalence, 53
equivalent statements, A-2
Erlanger Program, 320
Euclid, 319
even functions, 105, 150
even polynomials, 463
extended, linearly, 194
external direct sum, 183
factor, 399
field, 153–154
definition, 153
finite-dimensional vector space, 129
flat, k-flat, 40
free variable, 13
full column rank, 143
full row rank, 143
function, A-7
inverse image, 201
argument, A-7
bean diagram, A-7
codomain, A-7
composition, 238, A-7
correspondence, A-9
distance-preserving, 319
domain, A-7
even, 105
extended linearly, 194
identity, A-8
image, A-7
inverse, 255, A-8
left inverse, 255
multilinear, 338
odd, 105
one-to-one, A-8
onto, A-8
range, A-7
restriction, A-9
right inverse, 255
structure preserving, 175, 179
see homomorphism 191
two-sided inverse, 255
value, A-7
well-defined, A-7
zero, 192
Fundamental Theorem
of Algebra, 400
of Linear Algebra, 294
Gauss’s Method, 3
accuracy, 72–75
back-substitution, 5
by matrix multiplication, 250
elementary operations, 5
Gauss-Jordan, 51
Gauss-Jordan Method, 51
Gaussian elimination, 3
generalized null space, 427
generalized range space, 427
generated, 27
generated by, 27
geometric multiplicity, 418
Geometry of Linear Maps, 301–307
Google matrix, 472
Gram-Schmidt process, 280–285
graphite, 156
historyless process, 314
homogeneous coordinate vector, 383, 392
homogeneous coordinates, 324
homogeneous equation, 24
homomorphism, 191
composition, 238