























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.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。