K-Primitivity : A Literature Survey

2024/01/29 by Monimala Nej, Nej, Monimala
Computer Science · Social Sciences · Physics and Astronomy · #Cooperative Communication and Network Coding #Digital Marketing and Social Media #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.2402.18586

Abstract

A nonnegative matrix A is said to be primitive if there exists a positive integer m such that entries in A^m are positive and smallest such m is called the exponent of A: Primitive matrices are useful in the study of finite Markov chains theory. In 1998, in the context of finite Markov chains, Ettore Fornasini and Maria Elena Valcher [6] extended the notion of primitivity for a nonnegative matrix pair (A;B) by considering a positive discrete homogeneous two-dimensional (2D) state model. Further generalization to this notion of primitivity for k-tuple (A1;A2;...;Ak) of nonnegative matrices A1;A2;...;Ak is quite natural and known as k-primitivity. In this paper we present various results on k-primitivity given by different researchers from time to time.

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