Identity Matrices in Matlab

In this lesson, I will explain how to generate an identity matrix in Matlab.

So, what is an identity matrix? An identity matrix ( unit matrix ) is a square matrix with elements equal to 1 on the main diagonal and 0 elsewhere. For example, here's a 3x3 identity matrix: $$ I = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} $$

To generate an identity matrix in Matlab, you can use the eye(n) function.

eye(n)

where 'n' is the number of rows/columns of the square matrix.

Let's take a look at a practical example.

To create a 2x2 identity matrix, simply type eye(2)

>> eye(2)

This command will create a 2x2 identity matrix.

ans =
1 0
0 1

Similarly, to create a 3x3 identity matrix, type eye(3)

>> eye(3)

The result will be a 3x3 identity matrix.

ans =
1 0 0
0 1 0
0 0 1

You can define an identity matrix of any size using this approach.

In addition, the eye(m,n) function with two parameters allows you to create a rectangular matrix that includes an identity matrix as a square submatrix.

eye(m,n)

where 'm' is the number of rows and 'n' is the number of columns of the rectangular matrix.

For example, to create a 2x3 matrix with an identity submatrix, type eye(2,3)

>> eye(2,3)

Matlab will generate a rectangular matrix with an identity matrix inside.

ans =
1 0 0
0 1 0