Extract a diagonal from a matrix in Octave

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

What is the diagonal of a matrix? They are the elements that are on the main diagonal of the matrix.For example, the main diagonal of this matrix are the elements 1, 5, 9. $$ M = \begin{pmatrix} \color{red}1 & 2 & 3 \\ 4 & \color{red}5 & 6 \\ 7 & 8 & \color{red}9 \end{pmatrix} $$

I'll give you a practical example.

Create a 3x3 square matrix with three rows and three columns.

>> M=[1 2 3; 4 5 6; 7 8 9]
M =
1 2 3
4 5 6
7 8 9

To know the number of elements in the main diagonal type diag(M)

>> diag(M)
ans =
1
5
9

The elements in the main diagonal of the matrix are the numbers 1, 5 and 9

$$ M = \begin{pmatrix} \color{red}1 & 2 & 3 \\ 4 & \color{red}5 & 6 \\ 7 & 8 & \color{red}9 \end{pmatrix} $$

To know the elements on the diagonal above the main diagonal type diag(M,1)

>> diag(M,1)
ans =
2
6

This command extracts the numbers 2 and 6 that are on the diagonal above the main one.

$$ M = \begin{pmatrix} 1 & \color{red}2 & 3 \\ 4 & 5 & \color{red}6 \\ 7 & 8 & 9 \end{pmatrix} $$

Now type diag(M,2)

>> diag(M,2)
ans = 3

This way you get the elements on the diagonal even higher and so on.

$$ M = \begin{pmatrix} 1 & 2 & \color{red}3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} $$

To extract the elements of the diagonal under the main diagonal type diag(M,-1)

>> diag(M,-1)
ans =
4
8

This command extracts the elements under the main diagonal.

$$ M = \begin{pmatrix} 1 & 2 & 3 \\ \color{red}4 & 5 & 6 \\ 7 & \color{red}8 & 9 \end{pmatrix} $$

If you want to delete all other elements, except those on the main diagonal, type diag(diag(M))

>> diag(diag(M))
ans =
Diagonal Matrix
1 0 0
0 5 0
0 0 9

This way you get a diagonal matrix.

$$ M = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 9 \end{pmatrix} $$

If you want to extract the antidiagonal or secondary diagonal, flip the matrix by fliplr() function

Type diag(fliplr(M))

>> diag(fliplr(M))
ans =
3
5
7

This command returns the elements on the antidiagonal of the matrix

$$ M = \begin{pmatrix} 1 & 2 & \color{red}3 \\ 4 & \color{red}5 & 6 \\ \color{red}7 & 8 & 9 \end{pmatrix} $$

You can also use the diag () command to extract the elements of a rectangular array.

For example, create a rectangular matrix with 3 rows and 4 columns.

>> M2=[1 1 1 1 ; 2 2 2 2 ; 3 3 3 3]
M2 =
1 1 1 1
2 2 2 2
3 3 3 3

Now type diag(M2)

>> diag(M2)
ans =
1
2
3

This command extracts the elements on the diagonal of the square matrix into the rectangular matrix.

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