Primitive matrices over polynomial semirings |
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Authors: | Shigeki Akiyama Horst Brunotte |
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Institution: | 1. Department of Mathematics, Faculty of Science Niigata University, Ikarashi 2-8050, Niigata 950-2181, Japan;2. Haus-Endt-Strasse 88, D-40593 Düsseldorf, Germany |
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Abstract: | An extension of the definition of primitivity of a real nonnegative matrix to matrices with univariate polynomial entries is presented. Based on a suitably adapted notion of irreducibility an analogue of the classical characterization of real nonnegative primitive matrices by irreducibility and aperiodicity for matrices with univariate polynomial entries is given. In particular, univariate polynomials with nonnegative coefficients which admit a power with strictly positive coefficients are characterized. Moreover, a primitivity criterion based on almost linear periodic matrices over dioids is presented. |
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