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A matrix is a two-dimensional array of numbers.
In MATLAB, you create a matrix by entering elements in each row as comma or space delimited numbers and using semicolons to mark the end of each row.
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 will execute the above statement and return the 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 an element in the mth row and nth column, of a matrix mx, we write −
mx(m, n);
For example, to refer to the element in the 2nd row and 5th column, of the matrix a, as created in the 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 will execute the above statement and return the following result −
ans = 6
To reference all the elements in the mth column we type A(:,m).
Let us create a column vector v, from the 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 will execute the above statement and return the following result −
v =
4
5
6
7
You can also select the elements in the mth through nth columns, for this we write −
a(:,m:n)
Let us create a smaller matrix taking the elements from the 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]; a(:, 2:3)
MATLAB will execute the above statement and return the following result −
ans =
2 3
3 4
4 5
5 6
In the same way, you can create 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 will execute the above statement and return the following result −
ans =
2 3
3 4
4 5
5 6
In the same way, you can create 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 will execute the above statement and return the following result −
sa =
3 4 5
4 5 6
Deleting a Row or a Column in a Matrix
You can delete an entire row or column of a matrix by assigning an empty set of square braces [] to that row or column. Basically, [] denotes an empty array.
For example, let us delete the fourth row 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 will execute the above statement and return the following result −
a =
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
Next, let us delete the fifth column of a −
a = [ 1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7; 4 5 6 7 8]; a(: , 5)=[]
MATLAB will execute the above statement and return the following result −
a =
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 7
Example
In this example, let us create a 3-by-3 matrix m, then we will copy the second and third rows of this matrix twice to create a 4-by-3 matrix.
Create a script file with the following code −
a = [ 1 2 3 ; 4 5 6; 7 8 9]; new_mat = a([2,3,2,3],:)
When you run the file, it displays the following result −
new_mat =
4 5 6
7 8 9
4 5 6
7 8 9
Matrix Operations
In this section, let us discuss the following basic and commonly used matrix operations −
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