## Sunday, September 30, 2018

### Advanced Math Solutions - Matrix Trace Calculator, Matrix Trace

In today’s blog post, we will go over how to calculate the trace of a matrix. However, first, it is important to go over what the diagonal of a matrix is.

The main diagonal of an n x n matrix consists of entries whose row number is the same as its column number. In an n x n matrix, the diagonal is a_(1,1),a_(2,2),...,a_(n,n).
Below is a matrix with its diagonal circled.

The trace of an n x n matrix is the sum of all the entries on the main diagonal. The trace of a matrix, A, is denoted \tr(A). (Note: In order to calculate the trace of a matrix, the matrix must have the same number of rows and columns. Otherwise, there is no main diagonal.)

Let’s see some examples to better understand.

First example (click here):

1. Identify the main diagonal

2. Sum all the entries on the main diagonal

Next example (click here):

1. Identify the main diagonal

2. Sum all of the entries on the main diagonal

Last example (click here):

1. Identify the main diagonal

2. Sum all of the entries on the main diagonal

Calculating the trace of a matrix is pretty easy. Just make sure to remember what the definition of the trace of a matrix is. For more help or practice on this topic, check out Symbolab’s Practice, which has more practice problems and quizzes.

Until next time,

Leah