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