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# Matrix congruence can be seen as the change of basis of a bilinear form

nosplit "Congruent matrix" words: 41
From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis modifies the matrix representation of a bilinear form as: $$CTMC (49)$$
So, by taking , we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.