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
