View source for 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 [[bilinear form]] or [[quadratic form]] with respect to different bases, the change of basis matrix being $P$.


====References====
* P.M. Cohn, "Basic Algebra: Groups, Rings and Fields", Springer (2004) ISBN 1852335874  {{ZBL|1003.00001}}