Abstract
Abstract. 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. 1.
Keywords
MathematicsHermitian matrixCongruence (geometry)SkewPure mathematicsPolynomialCombinatoricsAlgebra over a fieldMathematical analysisGeometry
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Publication Info
- Year
- 2003
- Type
- article
- Volume
- 10
- Issue
- 1
- Pages
- 1-10
- Citations
- 17
- Access
- Closed
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Cite This
Dragomir Ž. Djoković,
Fernando Szechtman
(2003).
Solution of the congruence problem for arbitrary hermitian and skew-hermitian matrices over polynomial rings.
Mathematical Research Letters
, 10
(1)
, 1-10.
https://doi.org/10.4310/mrl.2003.v10.n1.a1
Identifiers
- DOI
- 10.4310/mrl.2003.v10.n1.a1