Department of Mathematics

Math 300: Mathematical Computing

Matlab Cheat Sheet

Defining Matrices

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

A = [1 2; 3 4]


A=[1 2

3 4]

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


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'


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

Special Functions

Trig functions




Zero matrix

N x N zero matrix

M x N zero matrix




Identity matrix eye(N)

Random matrix

N x N random matrix with entries between 0 and 1

M x N random matrix





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')

Saving and Loading

Save current variables in "matlab.mat" save
Save current variables in "myfile.mat" save myfile
Load variables from "matlab.mat" load
Load variables from "myfile.mat" load myfile
Read comma-delimited data from "myfile.csv" dlmread('myfile.csv',',')
Read space-delimited data dlmread('myfile.csv',' ')


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


The last test will take place at the final exam time on Tuesday, 12 December, from 1:30-3:30. It will be written as a one-hour (not 50 minute) exam, but you may have the full two hours for it. In other respects it will be very like the other tests, but comprehensive - it will emphasize Python, but cover all the topics we have seen. There is a Sample Exam, but be aware that things will have changed somewhat with the advent of ChatGPT.

Assignment A is posted.

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