Trace Tricks

The trace of a square matrix is the sum of the elements on the main diagonal. That is, for an n by n square matrix A, the trace of A is $$\mathrm{tr}(A) = \sum_{i=1}^n A_{ii} .$$ This might not seem too exciting at first. However, the trace operator has a neat quasi-commutative property: for matrices U and V, so long as the internal dimensions work out, it … [Read more…]