Abstract
A new proof is presented that any bilinear form b(x, y) on a finite-dimensional vector space is equivalent to its transposed form b(y, x), or again that any square matrix over a field is congruent to its transpose. This result is then applied to show that a certain previously studied class of rings possess an antiautomorphism.
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Williams, G.D. The Congruence of a Matrix with its Transpose. Results. Math. 47, 147–154 (2005). https://doi.org/10.1007/BF03323020
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DOI: https://doi.org/10.1007/BF03323020