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MATLAB - MATRIX
A matrix is a two-dimensionalarray of numbers.
InMATLAB, youcreate a matrix by entering elements ineachrow as comma or space delimited numbers and
using semicolons to mark the end of eachrow.
For example, let us create a 4-by-5 matrix a:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]
MATLAB willexecute the above statement and returnthe following result:
a =
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
Referencing the Elements of a Matrix
To reference anelement inthe mth row and nth column, of a matrix mx, we write:
mx(m, n);
For example, to refer to the element inthe 2nd row and 5th column, of the matrix a, as created inthe last section,
we type:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(2,5)
MATLAB willexecute the above statement and returnthe following result:
ans =
6
To reference allthe elements inthe mth columnwe type A(:,m).
Let us create a columnvector v, fromthe elements of the 4th row of the matrix a:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
v = a(:,4)
MATLAB willexecute the above statement and returnthe following result:
v =
4
5
6
7
Youcanalso select the elements inthe mth throughnth columns, for this we write:
a(:,m:n)
Let us create a smaller matrix taking the elements fromthe second and third columns:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];](https://image.slidesharecdn.com/matlabmatrics-150713153324-lva1-app6892/85/Matlab-matrics-1-320.jpg)
![a(:, 2:3)
MATLAB willexecute the above statement and returnthe following result:
ans =
2 3
3 4
4 5
5 6
Inthe same way, youcancreate a sub-matrix taking a sub-part of a matrix.
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(:, 2:3)
MATLAB willexecute the above statement and returnthe following result:
ans =
2 3
3 4
4 5
5 6
Inthe same way, youcancreate a sub-matrix taking a sub-part of a matrix.
For example, let us create a sub-matrix sa taking the inner subpart of a:
3 4 5
4 5 6
To do this, write:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
sa = a(2:3,2:4)
MATLAB willexecute the above statement and returnthe following result:
sa =
3 4 5
4 5 6
Deleting a Row or a Column in a Matrix
Youcandelete anentire row or columnof a matrix by assigning anempty set of square braces [] to that row or
column. Basically, [] denotes anempty array.
For example, let us delete the fourthrow of a:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a( 4 , : ) = []
MATLAB willexecute the above statement and returnthe following result:
a =
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
Next, let us delete the fifthcolumnof a:
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
a(: , 5)=[]](https://image.slidesharecdn.com/matlabmatrics-150713153324-lva1-app6892/85/Matlab-matrics-2-320.jpg)
![MATLAB willexecute the above statement and returnthe following result:
a =
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 7
Example
Inthis example, let us create a 3-by-3 matrix m, thenwe willcopy the second and third rows of this matrix twice to
create a 4-by-3 matrix.
Create a script file withthe following code:
a = [ 1 2 3 ; 4 5 6; 7 8 9];
new_mat = a([2,3,2,3],:)
Whenyourunthe file, it displays the following result:
new_mat =
4 5 6
7 8 9
4 5 6
7 8 9
Matrix Operations
Inthis section, let us discuss the following basic and commonly used matrix operations:
Additionand Subtractionof Matrices
Divisionof Matrices
Scalar Operations of Matrices
Transpose of a Matrix
Concatenating Matrices
Matrix Multiplication
Determinant of a Matrix
Inverse of a Matrix](https://image.slidesharecdn.com/matlabmatrics-150713153324-lva1-app6892/85/Matlab-matrics-3-320.jpg)
Matlab matrics
- 1. http://www.tutorialspoint.com/matlab/matlab_matrics.htm Copyright © tutorialspoint.com MATLAB - MATRIX A matrix is a two-dimensionalarray of numbers. InMATLAB, youcreate a matrix by entering elements ineachrow as comma or space delimited numbers and using semicolons to mark the end of eachrow. For example, let us create a 4-by-5 matrix a: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8] MATLAB willexecute the above statement and returnthe following result: a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 4 5 6 7 8 Referencing the Elements of a Matrix To reference anelement inthe mth row and nth column, of a matrix mx, we write: mx(m, n); For example, to refer to the element inthe 2nd row and 5th column, of the matrix a, as created inthe last section, we type: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; a(2,5) MATLAB willexecute the above statement and returnthe following result: ans = 6 To reference allthe elements inthe mth columnwe type A(:,m). Let us create a columnvector v, fromthe elements of the 4th row of the matrix a: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; v = a(:,4) MATLAB willexecute the above statement and returnthe following result: v = 4 5 6 7 Youcanalso select the elements inthe mth throughnth columns, for this we write: a(:,m:n) Let us create a smaller matrix taking the elements fromthe second and third columns: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8];
- 2. a(:, 2:3) MATLAB willexecute the above statement and returnthe following result: ans = 2 3 3 4 4 5 5 6 Inthe same way, youcancreate a sub-matrix taking a sub-part of a matrix. a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; a(:, 2:3) MATLAB willexecute the above statement and returnthe following result: ans = 2 3 3 4 4 5 5 6 Inthe same way, youcancreate a sub-matrix taking a sub-part of a matrix. For example, let us create a sub-matrix sa taking the inner subpart of a: 3 4 5 4 5 6 To do this, write: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; sa = a(2:3,2:4) MATLAB willexecute the above statement and returnthe following result: sa = 3 4 5 4 5 6 Deleting a Row or a Column in a Matrix Youcandelete anentire row or columnof a matrix by assigning anempty set of square braces [] to that row or column. Basically, [] denotes anempty array. For example, let us delete the fourthrow of a: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; a( 4 , : ) = [] MATLAB willexecute the above statement and returnthe following result: a = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7 Next, let us delete the fifthcolumnof a: a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; a(: , 5)=[]
- 3. MATLAB willexecute the above statement and returnthe following result: a = 1 2 3 4 2 3 4 5 3 4 5 6 4 5 6 7 Example Inthis example, let us create a 3-by-3 matrix m, thenwe willcopy the second and third rows of this matrix twice to create a 4-by-3 matrix. Create a script file withthe following code: a = [ 1 2 3 ; 4 5 6; 7 8 9]; new_mat = a([2,3,2,3],:) Whenyourunthe file, it displays the following result: new_mat = 4 5 6 7 8 9 4 5 6 7 8 9 Matrix Operations Inthis section, let us discuss the following basic and commonly used matrix operations: Additionand Subtractionof Matrices Divisionof Matrices Scalar Operations of Matrices Transpose of a Matrix Concatenating Matrices Matrix Multiplication Determinant of a Matrix Inverse of a Matrix