Index

Symbols

./ .\* .^ .’ /, [1]

3-D plots :math:`l_1` norm :math:`l_2` norm \* \\, [1] ’

A

adaptive ODE algorithms angle between vectors anonymous functions ans area plot arrays

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

B

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

bidiag bidiagonal decomposition binomial distribution bisection root-finding boxplot bulge

C

Cardinality cast cell array central limit theorem change of basis 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] confidence interval, [1] contour contour3 convergence of eigenvalue algorithms convergence points convex function minimum convex optimization correlation covariance, [1] cr, [1] CR factorization cross 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] diag

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

E

Eckart–Young theorem economy SVD, [1] eig, [1], [2] eig22, [1] eigen-decomposition eigenpair eigenvalue eigenvalue properties eigenvector, [1] eigenvector properties eigFrancis eigQR, [1] element-wise operators elementary matrices

elimination elimination matrix elimination procedures end eps Euclidean norm Euler derivative Euler’s ODE method existence of the SVD theorem exp, [1] expand expm exponential distribution eye

F

factor fast Fourier transform (FFT) fft Fibonacci sequence, [1] figure fillmissing find for loop

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

G

gaussian distribution Gaussian elimination, [1] generalized eigendecomposition geometric transforms

givens, [1] Givens rotation matrix Gram–Schmidt Gram–Schmidt process

H

helper functions Hermitian matrix Hermitian transpose hess Hessenberg decomposition Hessenberg form Hessenberg matrix hessForm

Heun’s ODE method histogram hold off, [1] hold on, [1] homogeneous transformation matrix householder, [1] Householder reflection Householder reflector Householder transform

I

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

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

K

keywords

L

Laplace expansion least squares regression left null space left-divide, [1] left-divide operator legend limit limit - symbolic line plots linear equations linear independence

linear system applications linear vector properties linspace logical operators logical vectors logistic equation logspace lower triangular matrix LR algorithm lsqminnorm lu, [1], [2], [3] LU decomposition, [1]

M

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

mean, [1] 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 Newton root-finding Newton square root algorithm nexttile nnz norm, [1], [2], [3] normal distribution

normalized vector null, [1], [2], [3], [4] null space, [1] null space from the SVD number e numeric derivative numerical differential equations numerical integration numerical methods numerical stability, [1]

O

ODE ODE solver suite ODE stability omitnan ones orth, [1], [2] Orthogonal basis vectors orthogonal matrix

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

P

p-norm parametric form partial pivoting PCA pi pie chart pinv, [1] pivot plot Plot Editor plot legend plot line colors plot line style plot markers plot matrix data plot3 plotting data

poly polyfit polynomial roots, [1] poorly condition matrix positive definite matrix power method powers of matrix pre-defined constants preallocating storage private functions Probability Distributions product of eigenvalues corollary product of transposes projection, [1], [2] properly Hessenberg pseudo-inverse, [1] public functions

Q

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

QR factorization QR step qrFactor quartile quasitriangular matrix QZ algorithm

R

rand randi randn random numbers rank, [1], [2], [3], [4], [5] rank from the singular values theorem Rayleigh quotient rcond rcond number readtable real real eigenvalues of a symmetric matrix theorem reduced row echelon form, [1], [2] reflection matrix relational operators right hand rule, [1]

right null space right-divide right-divide operator RKF45 ODE method roots, [1], [2] roots of a function, [1] roots of a polynomial, [1] rotation matrix round-off errors, [1] row exchanges row space row vector, [1] row view of systems RREF rref, [1], [2], [3], [4], [5] Runge-Kutta ODE method Runge-Kutta-Fehlberg method

S

scalar scatter plot Schur decomposition Schur triangularization theorem schurFrancis secant root-finding selection statements sequence short circuit evaluation similar matrices theorem similarity transform simplify Simpson’s rule singular singular matrix, [1] Singular Value Decomposition solve sort span, [1] sparse matrices spectral decomposition spectral decomposition theorem spectral derivative spectral theorem stair step plot standard deviation

statistical population statistical sampling statistical significance statistics std steady state stem plot stiff ODE string subplot subs, [1] subspace iteration sum sum of eigenvalues corollary surf surfc surfl SVD, [1] svd SVD!economy, [1] svd65 svdFrancis switch switch–case symbolic math symmetric matrix, [1] systems of ODE

T

t-test table testing eigensystem correctness text (plotting) tic tick marks tiledlayout

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

U

under-determined systems uniform distribution unit vector

unitary matrix upper triangular matrix UTeigVect, [1]

V

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

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

W

waterfall

while loop Wilkinson shift, [1]

X

xlim	xticklabels xticks

Y

ylim	yticklabels yticks

Z

Z critical value, [1] z-test

zero matrix zeros, [1]