Diagonal matrix in Octave

In this lesson I'll explain how to create a diagonal matrix in Octave.

What is the diagonal matrix? It is a square matrix where the elements on the main diagonal are different from zero. All other elements of the matrix are null. This is an example of a diagonal matrix $$ M = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 4 \end{pmatrix} $$

I'll give you a practical example.

Create a number vector with 4 elements.

>> v=[1 2 3 4]
v =
1 2 3 4

Now type the command diag(v)

The output result is a 4x4 diagonal matrix with four rows and four columns.

>> diag(v)
ans =
Diagonal Matrix
1 0 0 0
0 2 0 0
0 0 3 0
0 0 0 4

The elements on the main diagonal of the matrix are the numbers 1, 2, 3, 4 that you indicated in the vector

All other elements of the matrix are null.

$$ M = \begin{pmatrix} \color{red}1 & 0 & 0 & 0 \\ 0 & \color{red}2 & 0 & 0 \\ 0 & 0 & \color{red}3 & 0 \\ 0 & 0 & 0 & \color{red}4 \end{pmatrix} $$

You can also get the same result by typing diag([1 2 3 4]) without defining a vector.

>> diag([1 2 3 4])
ans =
Diagonal Matrix

1 0 0 0
0 2 0 0
0 0 3 0
0 0 0 4

To create a 3x3 diagonal matrix type diag([3 4 1])

>> diag([3 4 1])
ans =
Diagonal Matrix
3 0 0
0 4 0
0 0 1

This way you can define any diagonal matrix.