Page 258 - Linear Algebra Done Right

Index
250
linear dependence lemma,
Euclidean inner product,
25
100
linear functional, 117
field, 3 linear map, 38
finite dimensional, 22 linear span, 22
functional analysis, 23 linear subspace, 13
fundamental theorem of linear transformation, 38
algebra, 67 linearly dependent, 24
linearly independent, 23
generalized eigenvector, list, 4
164
Gram-Schmidt procedure, matrix, 48
108 matrix of a linear map, 48
matrix of a vector, 52
Hermitian, 128 matrix of an operator, 82
homogeneous, 47 minimal polynomial, 179
monic polynomial, 179
identity map, 38
multiplicity of an eigenpair,
identity matrix, 214 205
image, 43 multiplicity of an eigenvalue,
imaginary part, 69 171
infinite dimensional, 23
injective, 43 nilpotent, 167
inner product, 99 nonsingular matrix, 214
inner-product space, 100 norm, 102
integral, 241 normal, 130
invariant, 76 null space, 41
inverse of a linear map, 53
inverse of a matrix, 214 one-to-one, 43
invertible, 53 onto, 44
invertible matrix, 214 operator, 57
isometry, 147 orthogonal, 102
isomorphic, 55 orthogonal complement,
111
Jordan basis, 186 orthogonal operator, 148
orthogonal projection, 113
kernel, 41 orthonormal, 106
orthonormal basis, 107
length, 4
linear combination, 22 parallelogram equality, 106