Is there a way to interpret "congruence " of matrices or linear maps? For example, "similar" maps can be interpreted as the same maps wrt different bases. Is there something like that corresponding to "congruent" maps?
Added: I have found on wikipedia that it means changing basis on the Gram matrix attached to a bilinear form, how is this different from the change of basis for normal linear maps? and why does using transposes work?
Thank you.