Page 218 - Matrices theory and applications

Hermitian, 40
p
l ,61
positive definite, 42
Hermitian adjoint, 40
algebra, 65, 70
Frobenius, 182
Hessenberg, 169
induced, 65
idempotent, 6
identity, 5
matrix, 65
inverse, 20
Schur, 131
invertible, 20 norm Index 201
Schur’s, 59, 182
nilpotent, 6 subordinated, 65
nonnegative, 80 norms
nonsingular, 20 equivalent, 63
normal, 40
orthogonal, 10 orthogonal
orthostochastic, 89 group, 20, 120
permutation, 5 subspace, 11
projection, 32 orthogonally
regular, 20 diagonalizable, 48
singular, 20
skew-Hermitian, 40 Perron–Frobenius
skew-symmetric, 10 theorem, 81, 82
square, 5 Pfaffian, 22
stochastic, 87 polar decomposition, 115
bi-, 87 polynomial
symmetric, 10 invariant, 104
positive definite, 42 standard, 38
totally positive, 35 preconditioning, 165
transposed, 10 product
triangular, 5 Hadamard, 59
block-, 10 of matrices, 6
strictly, 5 scalar, 11
tridiagonal, 155 projector, 32
unitary, 41
method range, 7, 8
QR , 173 rank, 5
power decomposition, 104
inverse, 188 Rayleigh
conjugate gradient, 159 ratio, 48
Gauss–Seidel, 152 translation, 180
Jacobi, 151, 181 reductibility, 30
Leverrier, 188 relaxation
power, 185 method, 152
relaxation, 152 residue, 160
minimal polynomial, 27 Rieszthorin
minor, 17 theorem, 68
leading principal, 17 ring
principal, 17, 137 factorial, 99
Moore–Penrose Noetherian, 98
inverse, 145 principal ideal domain, 97