# Whats the "trace" of a Matrix?

Feb 12, 2017

Trace of a square matrix is the sum of the elements on the main diagonal.

#### Explanation:

Trace of a matrix is defined only for a square matrix .

It is the sum of the elements on the main diagonal, from the upper left to the lower right, of the matrix.

For example in the matrix $A$

$A = \left(\begin{matrix}\textcolor{red}{3} & 6 & 2 & - 3 & 0 \\ - 2 & \textcolor{red}{5} & 1 & 0 & 7 \\ 0 & - 4 & \textcolor{red}{- 2} & 8 & 6 \\ 7 & 1 & - 4 & \textcolor{red}{9} & 0 \\ 8 & 3 & 7 & 5 & \textcolor{red}{4}\end{matrix}\right)$

diagonal elements, from the upper left to the lower right are

$3 , 5 , - 2 , 9$ and $4$

Hence $t r a c e A = 3 + 5 - 2 + 9 + 4 = 19$