Matrix Trace in Matlab

In this lesson, I will explain how to calculate the trace of a matrix in Matlab.

So, what exactly is the trace of a matrix? It is the sum of the elements on the main diagonal of the matrix. For example, in the 3x3 matrix $$ M= \begin{pmatrix} \color{red}1 & 2 & 3 \\ 4 & \color{red}5 & 6 \\ 7 & 8 & \color{red}9 \end{pmatrix} $$ The trace is equal to 15 $$ TR(M) = 1 + 5 + 9 = 15 $$

Let's take a practical example to understand better.

First, create a 3x3 matrix and assign it to the variable M.

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

To calculate the trace of the matrix, simply type trace(M).

>> trace(M)
ans = 15

The trace of the matrix is 15.

Verify. Now let's verify this. The sum of the elements on the main diagonal of the matrix $$ M= \begin{pmatrix} \color{red}1 & 2 & 3 \\ 4 & \color{red}5 & 6 \\ 7 & 8 & \color{red}9 \end{pmatrix} $$ The trace of matrix is 15 $$ TR(M)=1+5+9 = 15 $$

In Matlab, you can also calculate the trace of rectangular matrices.

For example, let's create a 2x3 matrix.

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

Then, simply type trace(M) to calculate the trace.

>> trace(M)
ans = 6

The trace of the matrix is 6.

Verify. Let's verify this. The sum of the elements on the main diagonal of the matrix $$ M= \begin{pmatrix} \color{red}1 & 2 & 3 \\ 4 & \color{red}5 & 6 \end{pmatrix} $$ The trace of matrix is 6 $$ TR(M)=1+5 = 6 $$

Using this approach, you can easily calculate the trace of any matrix in Matlab.