  We equip the complex polynomial algebra C[t] with the involution which is the
identity on C and 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 by 1 matrices and 2 by 2 matrices with zero
diagonal. Morevover, we show that if two n by 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 not
2.
