Index

Symbols

.* ./ .^ .’ /, [1]

2-norm 3-D plots ; \* \\, [1]

A

adaptive ODE algorithms angle between vectors ans area plot arrays

assignment statement associative property augmented matrix axis axis right hand rule, [1]

B

backslash operator bar graph basis vectors, [1], [2] bell curve distribution Bernoulli distribution bidiag

bidiagonal decomposition binomial distribution block diagonal matrices boxplot break bulge

C

case cast cell array change of basis, [1] characteristic equation characteristic matrix chol cholesky Cholesky decomposition, [1] clear code block collect colon operator column space, [1], [2] column vector column view of systems commutative property computing eigenvectors

cond condition number, [1], [2], [3] confidence intervals continue contour contour3 convergence of eigenvalue algorithms convergence points convex function minimum convex optimization correlation counting covariance, [1] cr, [1] CR factorization cross product cumsum CVX

D

daspect data types DC Circuit deflation degree one Francis step degree two Francis step delete data, [1] derivative derivatives - symbolic det, [1] determinant, [1], [2], [3], [4] diag, [1]

diagonal matrix diagonalization diff, [1], [2] difference equations differential equations differential equations - symbolic dimension, [1] disp, [1] division dot dot product dsolve

E

Eckart–Young theorem economy SVD, [1], [2] eig, [1], [2] eig22 eigen-decomposition eigendecomposition eigenvalue, [1], [2], [3] eigenvalue problem eigenvalue problem history eigenvalue properties eigenvector, [1], [2], [3] eigenvector properties eigenvectors eigQR, [1] element-wise operators

elementary matrices elimination, [1], [2] elimination matrix elimination procedures else elseif end eps, [1] error statement Euclidean norm Euler derivative exp expand exponential distribution eye

F

factor Fibonacci sequence, [1] figure fillmissing, [1] find for loop format fplot, [1], [2]

fprintf Francis algorithm, [1] Francis step Frobenius norm full rank, [1] function handles function roots, [1] functions, [1] fzero

G

gaussian distribution Gaussian elimination, [1] generalized eigendecomposition givens, [1]

Givens transform Gram--Schmidt process Gram–Schmidt grid

H

helper functions Hermitian Hermitian matrix Hermitian transpose hess Hessenberg decomposition Hessenberg form, [1]

Hessenberg matrix hessForm histogram hold off, [1] hold on, [1] householder Householder reflector Householder transform

I

identifiers identity matrix if ill-conditioned matrix implicit Q theorem implicitly shifted QR import independent eigenvectors independent vectors indexing arrays indices inner product, [1] input input statement int

integral integration - symbolic interp1 interpolate inv, [1], [2] inverse, [1], [2] inverse of matrix invertible test iscolumn isempty iskeyword ismatrix ismissing isrow isscalar isvector

K

keywords

L

Laplace expansion left null space left-divide, [1] left-divide operator legend limit - symbolic linear equations linear independence linear system applications linear vector properties

linspace load logical operators logical vectors logspace lower triangular matrix LR algorithm lsqminnorm lu, [1], [2], [3] LU decomposition, [1], [2]

M

machine epsilon Markov matrix math - analytic math - symbolic matrix, [1] matrix factorization matrix indices matrix inverse, [1], [2] matrix multiplication max mean

median mesh meshgrid meshz min minimum value missing data mldivide mode Moore-Penrose pseudo-inverse, [1] moving window statistics movmean

N

n choose k NaN nearly singular matrix nexttile nnz norm, [1], [2] normal distribution

normalized vector null, [1], [2], [3], [4], [5], [6] null space, [1] number e numerical analysis Numerical Differential Equations numerical methods numerical stability

O

ODE ode omitnan ones orth, [1], [2] orth function Orthogonal basis vectors orthogonal matrix, [1]

orthogonal matrix factoring orthogonal matrix subspaces orthogonally equivalent orthonormal columns orthonormal inverse/transpose orthonormal matrix outer Product over-determined over-determined systems

P

parametric form partial pivoting PCA pi pie chart pinv, [1], [2] pivot plot plot legend plot matrix data plot3 Poisson distribution

poly polynomial roots, [1] poorly condition matrix positive definite matrix power method powers of matrix pre-defined constants preallocating storage product of transposes projection, [1], [2] properly Hessenberg pseudo-inverse, [1]

Q

qd algorithm qr, [1] QR algorithm QR algorithm with implicit shifts QR decomposition, [1] QR decomposition!economy, [1]

QR factorization QR step qrFactor quad quartile quasitriangular matrix, [1] QZ algorithm

R

rand randi randn random numbers rank, [1], [2], [3], [4], [5], [6], [7] Rayleigh quotient rcond, [1] rcond number readtable real reduced row echelon form, [1], [2] reflection matrix relational operators right hand rule, [1] right null space

right-divide right-divide operator RKF45 method roots, [1], [2], [3] roots of a function, [1] roots of a polynomial, [1] rotation matrix round-off errors, [1] row exchanges row space row vector row vectors row view of systems rref, [1], [2], [3], [4], [5], [6] RREF|(

S

save scalar scatter plot Schur decomposition schurFrancis selection statements sequence similar matrices similarity transform, [1] simplify simpson's rule singular singular matrix, [1] Singular Value Decomposition singular value decomposition, [1] solve sort space span, [1], [2] sparse matrices spectral decomposition spectral derivative spectral theorem

stair step plot standard deviation statistical population statistical sampling statistical significance std stem plot string subplot subs, [1] subspace iteration sum surf surfc surfl SVD, [1] svd SVD!economy, [1] svd65 svdFrancis switch symbolic math symmetric matrix, [1] systems of ODE

T

table testing eigensystem correctness testing Schur decomposition testing SVD text (plotting) tic tick marks tiledlayout

timing code toc trace, [1], [2] transformation matrix transpose, [1] trapezoid rule triangular matrix, [1] tridiagonal matrix trigonometry functions

U

under-determined systems uniform distribution unit vector

unitary matrix, [1] upper triangular matrix UTeigVect

V

variable variance vecnorm vector, [1], [2] vector arithmetic

vector indices vector length vector space, [1] vectorized code vpa, [1]

W

waterfall while loop

Wilkinson shift, [1], [2] writetable

X

xlim	xticklabels xticks

Y

ylim	yticklabels yticks

Z

zero matrix

zeros

Symbols

’