## 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.

1. Identify the main diagonal

2. Sum all the entries on the main diagonal

1. Identify the main diagonal

2. Sum all of the entries on the main diagonal

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

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