Matrix congruence

In linear algebra, a branch of mathematics, called two square matrices A and B are congruent if there is an invertible matrix P such that:

It means to be transposed matrix. The congruence of matrices is an equivalence relation on the class of square matrices.

Equivalent can be defined that two matrices are congruent if they represent the same bilinear form with respect to two ( possibly different ) bases.

After sylvester between inertia set two symmetric matrices are congruent if and only if they have the same index of inertia. The index of inertia is the triple consisting of the number of positive, negative and zero eigenvalues.