Section 3.8 Trace
The trace of a (square) matrix is just the sum of all of its diagonal elements. In terms of components,
\begin{equation}
\mathrm{tr}(A)=\sum_i A_{ii}\text{.}\tag{3.8.1}
\end{equation}
For example, if
\begin{equation}
A=\left(\begin{array}{ccc}
1\amp 2\amp 3\\
4\amp 5\amp 6\\
7\amp 8\amp 9
\end{array} \right)\tag{3.8.2}
\end{equation}
then
\begin{equation}
\mathrm{tr}(A)=1+5+9=15\text{.}\tag{3.8.3}
\end{equation}
Try it for yourself by computing
\begin{equation}
\mathrm{tr}\left(\begin{array}{ccc}
1\amp 34\amp 5\\
23\amp 5\amp 98\\
132\amp 7\amp 9
\end{array} \right)\text{.}\tag{3.8.4}
\end{equation}