Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings

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dc.creatorDjokovic, D. Z.
dc.creatorSzechtman, F.
dc.date2002-06-10
dc.date.accessioned2026-07-07T12:53:15Z
dc.date.available2026-07-07T12:53:15Z
dc.descriptionWe 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0206104
dc.identifierhttp://arxiv.org/abs/math/0206104
dc.identifierMathematical Research Letters 10 (2003), 1-10
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223557
dc.subjectRings and Algebras
dc.subject15A57,15A63
dc.titleSolution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings
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