## IndexIndex

1-norm, vector
2-norm, matrix
2-norm, vector
$[ \cdot ]$
$\epsilon_{\rm mach}$
$\fl{ \cdot }$
$\gamma_n$
$\infty$-norm, vector
$\kappa(A)$
$\maxi( \cdot )$
$\overline x$
$\overline {~~}$
$\vert \cdot \vert$
$e_j$
$p$-norm, matrix
$p$-norm, vector
absolute value
ACM
Alternative Computational Model
axpy
backward error analysis, dot product
Basic Linear Algebra Subprograms
BLAS
catastrophic cancellation
Cauchy-Schwartz inequality
CGS
characteristic polynomial
chasing the bulge
Cholesky decomposition
Cholesky factor
Cholesky factorization
Cholesky factorization theorem
Classical Gram-Schmidt
complex conjugate
condition number
conjugate
consistent matrix norm
cubic convergence, Item
defective matrix
deflation
determinant
direction of maximal magnification, Item
distance
dot product, backward error analysis
eigenpair
eigenvalue
eigenvector
elementary elementary pivot matrix
equivalence style proof
error-invariant
Euclidean distance
floating point numbers
forward substitution
Frobenius norm
Gauss transform
Gaussian elimination
Gaussian elimination with row exchanges
Geometric multiplicity
Givens' rotation
Gram-Schmidt orthogonalization
Hermitian dot product
Hermitian inner product
Hermitian Positive Definite
Hermitian positive definite
hessenberg matrix
homogeneity (of absolute value), Item
homogeneity (of matrix norm), Item
homogeneity (of vector norm), Item
Householder transformation
Housev
HPD
Implicit Q Theorem
induced matrix norm
infinity norm
Jacobi algorithm (eigenvalues and vectors)
Jordan Canonical Form
left pseudo inverse
Legendre polynomials
linear convergence
linear least-squares
linear transformation
LLS
LU decomposition
LU factorization
LU factorization - existence
LU factorization algorithm (bordered)
LU factorization algorithm (left-looking)
LU factorization algorithm (right-looking)
LU factorization with complete pivoting
LU factorization with partial pivoting
LU factorization with partial pivoting (right-looking algorithm)
LU factorization with pivoting
machine epsilon
magnitude
matrix
matrix 2-norm
matrix $p$-norm
matrix norm
matrix norm, 2-norm
matrix norm, $p$-norm
matrix norm, consistent
matrix norm, Frobenius
matrix norm, induced
matrix norm, submultiplicative
matrix norm, subordinate
matrix-vector multiplication
Method of Multiple Relatively Robust Representations (MRRR)
Method of Normal Equations
method of normal equations
MRRR
norm
norm, Frobenius
norm, infinity
norm, matrix
norm, vector
normal equations
numerical stability
orthogonal matrix
orthogonal projection
orthogonal vectors
orthonormal matrix
orthonormal vectors
parent functions, Item
partial pivoting
pivot
pivot element
positive definite
positive definiteness (of absolute value), Item
positive defnitenessx (of matrix norm), Item
positive defnitenessx (of vector norm), Item
precondition, Item
pseudo inverse
pseudo-inverse
QR algorithm
QR decomposition
QR Decomposition Theorem
QR factorization
Rank-Revealing QR
Rayleigh quotent
Rayleigh-quotient iteration
reflector
residual
right pseudo inverse
rowl pivoting
RRQR
Schur decomposition
Schur Decomposition Theorem
SCM
shifted QR algorithm
similarity transformation
Singular Value Decomposition
solving triangular systems
Spectral decomposition
spectral decomposition
Spectral Decomposition Theorem
spectrum
stability
standard basis vector
Standard Computational Model
submultiplicative matrix norm
subordinate matrix norm
superlinear convergence, Item
SVD
symmetric positive definite
The Francis implicit QR Step
The implicit Q theorem
triangle inequality (for absolute value)), Item
triangle inequality (for matrix norms)), Item
triangle inequality (for vector norms)), Item
triangular system
Tridiagonal matrix
unit ball
unit roundoff
unit roundoff error
unitary matrix
unitary similarity transformation
upper hessenberg matrix
Vandenmonde matrix
vector 1-norm
vector 2-norm
vector $\infty$-norm
vector $p$-norm
vector norm
vector norm, 1-norm
vector norm, 2-norm
vector norm, $\infty$-norm
vector norm, $p$-norm
Wilkinson shift, Item