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Index Index

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