we know a square matrix is similar to its transpose, this result holds true over any field. for they have the same "invariant factors".

Similarly, it has been proven that a square matrix is congruent to its transpose too. but the known proof of this result needs highly convoluted math. I wonder whether there is also something invariant under congruence or not. And with this we can give an elementary proof of this result.

for a proof of "A square matrix is congruent to its transpose"

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