Congruent matrices

Matrices $A$, $B$ over a ring $R$ for which there exists an invertible matrix $P$ such that $B = P^t A P$, where $P^t$ denotes the transposed matrix of $P$. Congruence of matrices is an equivalence relation. Congruence arises when $A$, $B$ represent a quadratic form with respect to different bases, the change of basis matrix being $P$.