Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings
Dragomir Ž. Djoković, Fernando Szechtman · Mathematical Research Letters · 2003
Let * be the involutorial automorphism of the complex polynomial algebra C[t] which sends t to -t.Answering a question raised by V.G.Kac, we show that every hermitian or skew-hermitian matrix over this algebra is congruent to the direct sum of 1×1 matrices and 2×2 matrices with zero diagonal.Moreover we show that if two n × n hermitian or skew-hermitian matrices have the same invariant factors, then they are congruent.The complex field can be replaced by any algebraically closed field of characteristic = 2.