# Congruent matrices

From Encyclopedia of Mathematics

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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

**How to Cite This Entry:**

Congruent matrices.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Congruent_matrices&oldid=54452