Matrix Manipulation in Matlab
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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.
![Matlab
MATRIX
>> A = [1 2 3; 4 5 6 ;7 8 9]
A =
1 2 3
4 5 6
7 8 9](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-3-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-4-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-5-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-6-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-7-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-8-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-12-320.jpg)
![Matlab
MATRIX CONCATENATION
>> B=[1 2;3 4]
B =
1 2
3 4](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-15-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-16-320.jpg)
![Matlab
DELETING ROWS AND COLUMNS
>> C(:,2)=[]
C =
1 1 2
3 3 4
5 0 1
7 2 3](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-17-320.jpg)
![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](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-18-320.jpg)
![Matlab
OBTAINING INFORMATION ABOUT
MATRIX PROPERTIES
>> [V,R] = max(B)
V =
7 9 8
R =
3 2 3](https://image.slidesharecdn.com/matrixmanipulationinmatlab-160228201821/85/Matrix-Manipulation-in-Matlab-20-320.jpg)
Matrix Manipulation in Matlab
- 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