Let $A,B$ be two rectangular $m\times n$ matrices related by $B= Q^t A P$ with $P$ an $n\times n$ and $Q$ an $m\times m $ matrix.
Is there a standard terminolgy for this relation? If instead of the transposed $Q^t$ one takes the inverse $Q^{-1}$ above, they are just called "equivalent" according to http://en.wikipedia.org/wiki/Matrix_equivalence
I know that when $m=n$ (Edit 1: and P=Q) one uses "congruent" (transposed case) and "similar" (inverse case).
Edit 2: $P$ and $Q$ are assumed both to be invertible (sorry for forgetting to write it). As Marc van Leeuwen pointed out, there is no point in distinguishing among the cases $Q$, $Q^t$ and $Q^{-1}$ since $Q$ is arbitrary ( and invertible). It only makes sense when interpreting $Q$ as coordinate change matrix and $A$ as a linear operator ( -> $Q^{-1}$) or bilinear form (-> $Q^t$) (see explanations of Paul Garrett).
Thanks to everybody who contributed to clarify my confused question.