## 1 Introduction

• MATLAB is a powerful computer programming language. It provides a data
analysis environment based on a Matrix Programming Language which is ideal
for mathematical and statistical applications. Softwares with similar purposes
include GAUSS, Splus, R and Ox.

• MATLAB can run in the edit mode (or interactive mode), ie, executing one com-
mand at a time, interactively. It also runs in the command mode (orbatchmode),
ie, running a long MATLAB program with a series of MATLAB commands.

• The MATLAB editor is a very is flexible and power.

• A MATLAB program consists of statements and commands. If a statement ends
with a semicolon (;) nothing is printed to the screen. If a statement ends without
a semicolon (;) the value of the variable denoted will be printed to the screen.
Here is a small example you can type in interactive mode
x=3;
x=3
z=7;
y=x+z;
a=[1 2 3]
a=[1; 2; 3]
• Routines (programs) in MATLAB end with the statement: return;
• Here is a small program that you can save in a file and execute.

## 2 Matrix Operations

Summation and substraction of matrices can be done when the two matrices are
of the same dimensions. The commands are
a=[1 2 3; 4 5 6];
b=[11 12 13;14 15 16];
c=a+b;
d=a-b;

• In linear algebra , matrix multiplications and matrix divisions should be done
with care. The commands are
a=[1 2 3; 4 5 6]; % a has 2 rows and 3 columns. Row 1 contains 1
b=[2 1 0;1 3 1;0 1 4];
c=a*b; % c will be a 2× 3 matrix}

• If X is a T×K matrix, then the element in the i-th row and j-th column is : X(i,j).
Scalars don’t need indexes. Vectors need only one index.

• X(:, 1:2) refers to all rows, columns 1 through 2 of matrix X.

• One important feature of MATLAB is element-by-element operations are allowed .
a=[1 2 3];
b=[2 3 4];
d=a+b; % a is added to the first row and the second row of b
e=a-b; % c is added to the three columns of b respectively
f=a.*b; % Element by element multiplication
g=a./b; % Element by element division
h=a. ^2 % Each element is squared

• Inverse a matrix: x=y’;

• Inverse a matrix: x=inv(y);

## 3 MATLAB Commands

• a=zeros(3,5); % a 3×5 matrix of zeros
• b=ones(2,4); % a 2×4 matrix of ones
• c=eye(4); % a 4×4 identity matrix
• d=i:k:j; % generating a sequence starting from i, advancing by k, stoping at j
• a=sum(x); % summation
• a=mean(x); % mean
• a=prod(x); % product
• a=median(x); % median
• a=sdt(x); % standard deviation
• a=max(x); % maximum
• a=min(x); % minimum

• a=exp(x); % exponential function
• a=log(x); % nature log function
• a=sqrt(x); % square root
• a=pi; % 3.1415926...
• a=gamma(x); % gamma function
• a=sin(x), cos(x), tan(x), arcsin(x); % trigonometric functions
• a=size(x); % dimension of matrix x
• a=length(x); % the size of the longest dimension of x
• a=det(x); % determinant of matrix x
• a=diag(x); % extracting the diagonal elements of matrix x
• y =filter(b,a,X); % This command is very useful in time series analysis and implements
the following

• rand(’seed’,sd); % set the seed of random number generator to sd
• randn(’seed’,sd); % set the seed of random normal generator to sd
• normpdf(x) % computes the density of a standard normal distribution
• R = normrnd(MU,SIGMA,m,n) % generates normal random numbers with pa-
rameters MU and SIGMA, where scalars m and n are the row and column di-
mensions of R

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