MATLAB - Matrix

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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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