Trace

The trace of an n b n matrix is the sum of the components along the main diagonal (that is, the diagonal that runs from the top left to the bottom). Written mathematically, the trace is

$\mathrm{tr}(A) =\sum_{i=1}^{n} a_{ii} = a_{11} + a_{22} + \dots + a_{(n-1)(n-1)} + a_{nn}$

For example:

$\mathrm{tr} \begin{bmatrix} 1 & 3 & 4 & 0 \\ 6 & 2 & 2 & 3 \\ 9 & 4 & 5 & 2 \\ 4 & 2 & 5 & 8 \end{bmatrix} = \sum_{i=1}^{4} a_{ii} = 1 + 2 + 5 + 8 = 16$

If the trace is equal to zero, the matrix is said to be traceless.