Dimension group of a non-negative integer irreducible matrix |
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Authors: | Lotfi Farhane,G rard Michon |
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Affiliation: | aDépartement de mathématiques, Faculté des sciences de Monastir, Boulevard de l’environnement, 5019 Monastir, Tunisia bInstitut de mathématiques de Bourgogne, B.P. 47870, 21078 Dijon Cedex, France |
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Abstract: | In this paper we are concerned with a non-negative integer and irreducible matrix . The main contribution is to prove that if the matrix satisfies certain spectral and algebraic constraints, the cone:is defined by linear maps , in the sense that v ∈ C is equivalent to, ϕl(v) ⩾ 0 for all l = 0, … , k − 1 (where k is the index of cyclicity of the irreducible matrix). This result allows us to characterize the dimension group generated by the matrix, it is a subgroup of endowed with an order induced by the positive cone of . |
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Keywords: | Non-negative matrices Dimension group |
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