This document provides an introduction to MATLAB. It discusses that MATLAB is a high-level language for technical computing where everything is a matrix and it is easy to perform linear algebra. It describes the MATLAB desktop interface and valid variable names. It also summarizes how to perform basic operations like addition, subtraction, multiplication, etc. on matrices and vectors. Finally, it outlines various matrix operations, statistical functions, random number generation, and plotting in MATLAB.

1. Introduction to MATLAB
Md. Menhazul Abedin
Lecturer, Statistics Discipline
Khulna university
menhaz70@gmail.com

2. What is MATLAB
• High level language for technical computing
• Stands for MATrix LABoratory
• Everything is a matrix - easy to do linear
algebra

3. MATLAB Desktop
Menu and toolbar
CommandHistory
Workspace

4. Valid variables Names
• A valid variable name starts with a letter,
followed by letters, digits, or underscores.
• MATLAB® is casesensitive, so A and a are not the
same variable.
• The maximum length of a variable name is the
value that the namelengthmax command returns.
• You cannot define variables with the same names
as MATLAB keywords, such as if or end. For a
complete list, run the iskeyword command.

5. Matlab keywords….
• Keywords are must not variable name
• 'break' 'case' 'catch' 'classdef' 'continue' 'else'
'elseif' 'end' 'for' 'function' 'global' 'if' 'otherwise'
'parfor' 'persistent' 'return' 'spmd' 'switch' 'try'
'while'

6. How to run?
• If program in command space press “ enter”
• If in open script then block command and
presss F9.

7. Matrices & Vectors
• All (almost) entities in MATLAB are matrices
• Easy to define:
• Use ‘,’ or ‘ ’ to separate row elements
• use ‘;’ to separate rows
>> A = [1 3; 5 8]
A = 1 3
5 8
>> A = [1,3; 5,8]
A = 1 3
5 8

8. Matrices & Vectors
• Order of Matrix -
– m=no. of rows,
– n=no. of columns
• Vectors - special cases
– n = 1 column vector
– m = 1 row vector

m  n

9. Simple algebraic operations
Addition +
Subtraction -
Multiplication *
Division /
Power ^
Logarithm log()
Exponential Exp()
Square root sqrt()
Absolute value abs()

10. Element wise operations…
.*element-by-element multiplication
./element-by-element division
.^ element-by-element power

11. Operators (relational, logical)
• == Equal to
• ~= Not equal to
• < Strictly smaller
• > Strictly greater
• <= Smaller than or equal to
• >= Greater than equal to
• & And operator
• | Or operator

12. Sequences…….
• t =1:10
t =
1 2 3 4 5 6 7 8 9 10
• k =2:-0.5:-1
k =
2 1.5 1 0.5 0 -0.5 -1
• y=[2:2:12]
y=
2 4 6 8 10 12
• B = [1:4; 5:8]
x =
1 2 3 4
5 6 7 8

13. Some practice…….
• Do some mathematical operations as like as
calculator (addition, subtraction,
multiplication, division, log, square root,
power and so on)

14. Matrix...
• a vector x = [1 2 5 1]
x =
1 2 5 1
• a matrix x = [1 2 3; 5 1 4; 3 2 -1]
x =
1 2 3
5 1 4
3 2 -1

15. Special matrix….
• Identity matrix= eye (row,column)
• One matrix= ones(row,column)
• Zero marix= zeros (row,column)

16. Matrix operations…
• Let A be a matrix….
• Determinant= det(A)
• Transpose= A’
• Rank = rank(A)
• Inverse= inv(A)
• Trace = trace(A)
• Eigen value=eig(A)
• Eigen value and vector= [V,D] = eig(A)
• Matrix multiplication= A*B
• Matrix multiplication= A.*B [elementwise]
• Singular values= svd(A)

17. Cont…
• diag diagonal atrix
• triu upper triangular matrix
• tril lower triangular matri
• rand randomly generated matrix
• C=rand(5,4)
• triu(C)
• tril(C)
• diag([0.9092;0.5163;0.2661])

18. Cont…
• Length of a vector= length(x)
• Size or dimension of matrix= size(A)
• Replication of same number=
repmat(number,m,n)

19. Basic statistical building function…
• Let be a sample
• Mean= mean(x)
• Median=median(x)
• Mode= mode(x)
• Variance=var(x)
• Standard deviation=std(x)
• Minimum= min(x)
• Maximum= max(x)
• Summation=sum(x)
nxxxx ,...,, 21

20. Data preprocessing…(Missing value)
• a = magic(3); a(2,2) = NaN
• a = 8 1 6
3 NaN 7
4 9 2
sum(a)
ans =
15 NaN 15
sum(a) ans = 15 NaN 15
sum(a,'omitnan')
ans = 15 10 15
Class of
variables=class(A)

21. Random number generation….
• Normal distribution:
normrnd(mu,sigma) for a single value
normrnd(mu,sigma,m,n) or
normrnd(mu,sigma[m,n]) for matrix having
m row and ncolumn
• Poisson distribution:
poissrnd(lamda)
poissrnd(lamda,m,n)
poissrnd(lamda,[m,n])
Binomial distribution:
binornd(N,P)
binornd(N,P,m,n)
binornd(N,P,[m,n])

22. Cont…
• Geometric distribution:
geornd(p)
geornd(p,m,n)
geornd(p,[m,n])
• Beta distribution:
betarnd(A,B)
betarnd(A,B,m,n)
betarnd(A,B,[m,n])
Exponential distribution:
exprnd(mu)
exprnd(mu,m,n)
exprnd(mu,[m,n])
Gamma distribution:
gamrd(A,B)
gamrnd(A,B,m,n)
gamrnd(A,B,[m,n])

23. Cont…
• Standard normal distribution:
randn return single value
randn(n) return n-by-n square matrix
randn(r,c) return r-by-c matrx

24. Covariance of Matrix
• C = cov(A,B)
returns the covariance between two random
variables A and B.
• C = cov(A)
returns the matrix of correlation
coefficient for A, where the columns
of A represent random variables and the rows
represent observations.

25. Example…
• A = [5 0 3 7; 1 -5 7 3; 4 9 8 10];
C = cov(A)
• A = [3 6 4]; B = [7 12 -9];
cov(A,B)

26. Correlation coefficient…
• R = corrcoef(A)
returns the matrix of correlation
coefficient for A, where the columns
of A represent random variables and the rows
represent observations.
• R= corrcoef(A,B)
returns coefficients between two random
variables A and B.

27. Example…..
• x = randn(6,1);
• y = randn(6,1);
• A = [x y 2*y+3];
• R = corrcoef(A)
• A = randn(10,1);
• B = randn(10,1);
• R = corrcoef(A,B)

28. Ploting…
• x vector
• y vector
• Z vector
plot(x,y) 2D line diagram
plot(x,y,z) 3D line diagram
scatter(x,y) scatter diagram
scatter(x,y,z) 3D scatter diagram
bar(x) bar diagram
bar3(x) 3D bar diagram
hist(x) histogram
boxplot(x) boxplot
• xlabel(‘text')
• ylabel(‘text')
scatter(x,y,'d')
scatter(x,y,'*')
scatter(x,y,'b')
scatter(x,y,'p')
scatter(x,y,’+')
scatter(x,y,‘x')
theta = linspace(0,1,500);
x = exp(theta).*sin(100*theta);
y = exp(theta).*cos(100*theta);
s = scatter(x,y)
You may change color like scatter(x,y,’x’,’r’)

29. Regression…
load moore
y=moore(:,6)
x1=ones(length(y),1)
x2=moore(:,1:5)
x=[x1 x2]
% now perform regression %
[b,bint,r,rint,stats]=regress(y,x)

30. Test…
• %Single mean test
load stockreturns
x = stocks(:,3)
length(x)
[h,p,ci,stats] = ttest(x)
load stockreturns
x = stocks(:,3);
h = ttest(x,0,0.01)
• %paired mean test
load examgrades
x = grades(:,1);
y = grades(:,2);
[h,p] = ttest(x,y)

31. Cont…
%paired mean test
load examgrades
x = grades(:,1);
y = grades(:,2);
[h,p] = ttest2(x,y)
load examgrades
x = grades(:,1);
y = grades(:,2);
[h,p] = ttest(x,y,0.01)
Similar way F-test , z-test, chi-square test etc
%t-Test for a Hypothesized Mean
load examgrades
x = grades(:,1);
h = ttest(x,75)
%One-Sided t-Test
load examgrades
x = grades(:,1);
h = ttest(x,65,'right')

32. ANOVA…
% ANOVA one way
y = meshgrid(1:5);
y = y + normrnd(0,1,5,5)
p = anova1(y)
%ANOVA two way........
load popcorn
popcorn
[p,tbl] = anova2(popcorn,3);

33. Importing data…
• Excel data
• Watch the vedio
• File import data fix direcory
open ( tick generate matlab code) next
finish
https://www.youtube.com/watch?v=-
mZci3mNjlU

34. • clc clear commad window
• whos data size, class, bytes etc
• who provide variable names
• help mean
• help who
• help median
• help regression
• help plot

35. Thanks