# Matlab Cheat Sheet

## Defining Matrices

Row vector x=[1 2 3]
Column vector x=[1 2 3]'
Matrix

A = [1 2; 3 4]

or

A=[1 2

3 4]

Transpose - use the apostrophe B = A'
Multiplication D = A*B

## Ranges

By integers from 0 to N x=0:N
By steps of .1 x=0:.1:N
Assign part of a matrix E(3:4,1:2) = A
Assign an entire column of a matrix F(:,1) = x'

## Sizes

Size of a matrix [m,n] = size(A)
Length of a vector n = length(x)

## Special Functions

Trig functions

sin(x)

cos(x)

etc.

Zero matrix

N x N zero matrix

M x N zero matrix

zeros(N)

zeros(M,N)

Identity matrix eye(N)

Random matrix

N x N random matrix with entries between 0 and 1

M x N random matrix

rand(N)

rand(M,N)

## Plotting

2-D plot with abscissae in x, ordinates in y plot(x,y)
2-D plot of sin(x) plot(x,sin(x))
2-D plot of sin(x) using green diamonds to indicate points plot(x,sin(x),'gd')

Save current variables in "matlab.mat" save
Save current variables in "myfile.mat" save myfile

## Eigenvalues

Eigenvalues of a matrix eig(A)
Eigenvalues and eigenvectors of A [evec,eval]=eig(A)
QR decomposition of a matrix [Q,R] = qr(A)

## Gauss elimination

LU decomposition of a matrix [L,U] = lu(A)
LU with a permutation matrix [L,U,P] = lu(A)
Cholesky decomposition of a symmetric matrix R = chol(A)
Solve Ax = b for x x = A\b

Assignment 7 is posted.

A solution to the exam has been posted.

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