K-本原性：文献综述
K-Primitivity : A Literature Survey
AI总结：
本文综述 k-本原性概念，从非负矩阵本原性及其 Markov 链应用出发，梳理其向矩阵对和 k 元组推广后的相关研究成果。
摘要：
非负矩阵 A 被称为本原矩阵，如果存在正整数 m，使得 A^m 中的所有元素均为正数，而最小的这种 m 称为 A 的指数。本原矩阵在有限 Markov 链理论研究中十分有用。1998 年，在有限 Markov 链背景下，Ettore Fornasini 和 Maria Elena Valcher [6] 通过考虑正离散齐次二维（2D）状态模型，将本原性概念推广到非负矩阵对 (A;B)。将这一本原性概念进一步推广到非负矩阵 A1、A2、…、Ak 的 k 元组 (A1;A2;…;Ak) 是相当自然的，并被称为 k-本原性。本文介绍了不同研究者陆续提出的关于 k-本原性的各种结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
