不可分非负矩阵、$M$ -矩阵及有限状态平稳马尔可夫链的嵌入问题
Infinitely divisible nonnegative matrices, $M$-matrices, and the embedding problem for finite state stationary Markov Chains
摘要：
本文详细讨论了有限状态平稳马尔可夫链的嵌入问题与$M$ -矩阵、非负矩阵的非负根之间的关系。证明了具有任意非负根的非奇异非负矩阵集是$\mathcal{IM}$中具有矩阵根的矩阵集的闭包。本文所提出的方法除了基本的矩阵分析外，并没有使用任何其他的方法，但是它回答了30多年前提出的关于$M$ -矩阵的一个问题，作为应用，得到了所有可嵌入随机阵的集合的一个新的特征作为推论。
英文摘要：
This paper explicitly details the relation between $M$-matrices, nonnegative roots of nonnegative matrices, and the embedding problem for finite-state stationary Markov chains. The set of nonsingular nonnegative matrices with arbitrary nonnegative roots is shown to be the closure of the set of matrices with matrix roots in $\mathcal{IM}$. The methods presented here employ nothing beyond basic matrix analysis, however it answers a question regarding $M$-matrices posed over 30 years ago and as an application, a new characterization of the set of all embeddable stochastic matrices is obtained as a corollary.
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。
