Abstract

FUJIMOTO, Takao  and  EKUNI, Fumiko. Indecomposability and Primitivity of Nonnegative Matrices. Polít. cult. [online]. 2004, n.21, pp.163-176. ISSN 0188-7742.

This paper deals with the propositions concerning the relationship between the indecomposability and the primitivity of nonnegative square matrices. The main theorem is that a nonnegative matrix is primitive if and only if its k-th power is indecomposable for any positive integer k. This result dates back to Frobenius. Two applications of the result are given, one is to Leslie model of population dinamycs and the other to social network analysis.

Keywords : indecomposability; primitivity; nonnegative matrices; Frobenius; Leslie model.

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