## IndexIndex

(Euclidean) length, Item
1-norm (vector), Item
1-norm, vector
2-norm (vector), Item
2-norm, matrix
2-norm, vector
$[ \cdot ]$
$\epsilon_{\rm mach}$
$\fl{ \cdot }$
$\gamma_n$
$\infty$-norm (vector), Item
$\infty$-norm, vector
$\kappa(A)$
$\maxi( \cdot )$
$\overline A$
$\overline x$
$\overline {~~}$
$\theta_j$
$\vert \cdot \vert$
$e_j$
$I$
$p$-norm (vector), Item
$p$-norm, matrix
$p$-norm, vector
absolute value
ACM
Alternative Computational Model
axpy
backward stable implementation
Basic Linear Algebra Subprograms
BLAS
blocked algorithm
catastrophic cancellation
Cauchy-Schwarz inequality
CGS
characteristic polynomial
chasing the bulge
Cholesky decomposition, Week
Cholesky factor
Cholesky factorization
Cholesky factorization theorem
Classical Gram-Schmidt
complex conjugate
complex product, Item
condition number
conjugate
conjugate (of matrix), Item
conjugate (of vector), Item
conjugate of a matrix
conjugate transpose (of matrix), Item
conjugate transpose (of vector), Item
consistent matrix norm
cost of basic linear algebra operations
cubic convergence
defective matrix
deflation
descent methods, Week
determinant
direction of maximal magnification, Item
distance
dot product
eigenpair
eigenvalue
eigenvector
elementary elementary pivot matrix
equivalence style proof
Euclidean distance
exact descent method
fill-in
fixed-point equation
FLAME notation
floating point numbers
forward substitution
Frobenius norm
Gauss transform
Gaussian elimination
Gaussian elimination with row exchanges
Geometric multiplicity
Givens' rotation
Gram-Schmidt orthogonalization
Hermitian
Hermitian Positive Definite
Hermitian positive definite
Hermitian transpose
Hermitian transpose (of matrix), Item
Hermitian transpose (of vector), Item
Hessenberg matrix
homogeneity (of absolute value), Item
homogeneity (of matrix norm)
homogeneity (of vector norm)
Householder reflector
Householder transformation
Housev
Housev1
HPD
identity matrix
Implicit Q Theorem
induced matrix norm
infinity norm
inner product
Jordan Canonical Form
Krylov subspace
left pseudo inverse
left pseudo-inverse
left singular vector
Legendre polynomials
linear convergence
linear least squares, Week
linear transformation
LLS, Week
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 1-norm, Item
matrix 2-norm
matrix $\infty$-norm, Item
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 p-norm, Item
matrix-vector multiplication
Method of Multiple Relatively Robust Representations (MRRR)
Method of Normal Equations
method of normal equations
MRRR
natural ordering, Item
nested dissection
norm, Week
norm, Frobenius
norm, infinity
norm, matrix
norm, vector
normal equations
numerical stability, Week
orthogonal matrix
orthogonal projection
orthogonal vectors
orthonormal matrix
orthonormal vectors
over-relaxation
parent functions, Item
partial pivoting
pivot
pivot element
positive definite
positive definiteness (of absolute value), Item
positive defnitenessx (of matrix norm)
positive defnitenessx (of vector norm)
precondition, Item
pseudo inverse
pseudo-inverse
QR algorithm
QR decomposition, Week
QR Decomposition Theorem
QR factorization, Week
QR factorization with column pivoting
Rank Revealing QR
Rayleigh quotent
Rayleigh Quotient Iteration
reflector
residual
right pseudo inverse
right singular vector
rotation
rowl pivoting
RRQR
Schur decomposition
Schur Decomposition Theorem
SCM
separator
shifted inverse power method
shifted QR algorithm
similarity transformation
Singular Value Decomposition
singular vector
solving triangular systems
SOR
sparse linear system, Week
Spectral decomposition
spectral decomposition
Spectral Decomposition Theorem
spectrum
stability, Week
standard basis vector
Standard Computational Model
submultiplicative matrix norm
subordinate matrix norm
subspace iteration
successive over-relaxation
superlinear convergence
SVD
symmetric positive definite
The Francis implicit QR Step
The implicit Q theorem
transpose
transpose (of matrix), Item
transpose (of vector), Item
triangle inequality (for absolute value)), Item
triangle inequality (for matrix norms))
triangle inequality (for vector norms))
triangular system
unit ball
unit roundoff
unit roundoff error
unitary matrix
unitary similarity transformation
upper Hessenberg matrix
Vandermonde matrix
vector 1-norm
vector 2-norm
vector $\infty$-norm, Item
vector $\infty$-norm
vector $p$-norm, Item
vector $p$-norm
vector norm
vector norm, 1-norm
vector norm, 2-norm
vector norm, $\infty$-norm
vector norm, $p$-norm
Wilkinson shift, Item