This document provides an overview of matrix manipulation in MATLAB. It discusses how to perform basic operations like addition, subtraction, and multiplication of matrices. It also covers transposing matrices, taking inverses, using colon operators to select rows and columns, generating matrices filled with zeros, ones, or random numbers, concatenating matrices, deleting rows and columns, and obtaining information about matrix properties using functions like size, ndims, and whos.

1. MATRIX MANIPULATION IN
MATLAB
Mohamed Loey

2. Matlab

3. Matlab
MATRIX
>> A = [1 2 3; 4 5 6 ;7 8 9]
A =
1 2 3
4 5 6
7 8 9

4. Matlab
Addition and Subtraction of Matrices
>> a = [ 1 2 3 ; 4 5 6; 7 8 9];
b = [ 7 5 6 ; 2 0 8; 5 7 1];
c = a + b
c =
8 7 9
6 5 14
12 15 10

5. Matlab
Scalar Operations of Matrices
>> a = [ 10 12 23 ; 14 8 6; 27 8 9];
b = 2;
c = a + b
c =
12 14 25
16 10 8
29 10 11

6. Matlab
Transpose of a Matrix
>> a = [ 10 12 23 ; 14 8 6; 27 8 9];
b = a’
b =
10 14 27
12 8 8
23 6 9

7. Matlab
Matrix Multiplication
>> a = [ 1 2 3; 2 3 4; 1 2 5];
b = [ 2 1 3 ; 5 0 -2; 2 3 -1];
prod = a * b
prod =
18 10 -4
27 14 -4
22 16 -6

8. Matlab
Inverse of a Matrix
>> a = [ 1 2 3; 2 3 4; 1 2 5];
inv(a)
ans =
-3.5000 2.0000 0.5000
3.0000 -1.0000 -1.0000
-0.5000 0 0.5000

9. Matlab
Colon Operator ‘:’
>>C3 = A(:,3)
C3 =
3
6
9

10. Matlab
Colon Operator ‘:’
>>R2 = A(2,:)
R2 =
4 5 6

11. Matlab
Colon Operator ‘:’
>>T2 = A(1:2,1:3)
T2 =
1 2 3
4 5 6

12. Matlab
GENERATING MATRICES
• zeros(M,N) generates an M x N matrix of zeros
• ones(M,N) generates an M x N matrix of ones
• rand(M,N) generates an M x N matrix whose
entries are uniformly-distributed random numbers
in the interval [0:0;1:0]
• randn(M,N) generates an M x N matrix whose
numbers are normally-distributed (i.e., Gaussian)
numbers with mean 0 and variance 1

13. Matlab
GENERATING MATRICES
>> K = 5*ones(3,3)
K =
5 5 5
5 5 5
5 5 5

14. Matlab
GENERATING MATRICES
>>B = rand(2,4)
B =
0.8147 0.1270 0.6324 0.2785
0.9058 0.9134 0.0975 0.5469

15. Matlab
MATRIX CONCATENATION
>> B=[1 2;3 4]
B =
1 2
3 4

16. Matlab
MATRIX CONCATENATION
>> C = [B B;B+4 B-1]
C =
1 2 1 2
3 4 3 4
5 6 0 1
7 8 2 3

17. Matlab
DELETING ROWS AND COLUMNS
>> C(:,2)=[]
C =
1 1 2
3 3 4
5 0 1
7 2 3

18. Matlab
OBTAINING INFORMATION ABOUT
MATRIX PROPERTIES
B = [5 1 2; 3 9 4; 7 6 8]
B =
5 1 2
3 9 4
7 6 8

19. Matlab
OBTAINING INFORMATION ABOUT
MATRIX PROPERTIES
>> max(B)
ans =
7 9 8

20. Matlab
OBTAINING INFORMATION ABOUT
MATRIX PROPERTIES
>> [V,R] = max(B)
V =
7 9 8
R =
3 2 3

21. Matlab
OBTAINING INFORMATION ABOUT
MATRIX PROPERTIES
The function size(A) returns a row
vector with components M and N
>> size(B)
ans = 3 3

22. Matlab
OBTAINING INFORMATION ABOUT
MATRIX PROPERTIES
The function ndims(A) returns the
number of dimension of the array.
>> ndims(B)
ans = 2

23. Matlab
Function whos
>> whos B
Name Size Bytes Class Attributes
B 3x3 72 double

24. Thanks For Listening
Mohamed Loey