I'm working on trace of matrices. Trace is defined for square matrix and there are some useful rule to deal with calculus (i.e. $tr(AB) = tr(BA)$, with $A$ and $B$ square, and more in general trace is invariant under cyclic permutation).
I was wondering if the formula $tr(AB) = tr(BA)$ holds even if $A$ and $B$ are rectangular, namely $A$ is n-by-m and $B$ is m-by-n.
I figured out that if one completes the involved matrices to be square by adding "zeros" where it is needed, then the formula still works...but I want to be sure of this thing!!! :D