Infinitely divisible nonnegative matrices, $M$-matrices, and the embedding problem for finite state stationary Markov Chains
Functional Analysis
2022-11-29 v2 Probability
Abstract
This paper explicitly details the relation between -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 . The methods presented here employ nothing beyond basic matrix analysis, however it answers a question regarding -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.
Cite
@article{arxiv.1709.09561,
title = {Infinitely divisible nonnegative matrices, $M$-matrices, and the embedding problem for finite state stationary Markov Chains},
author = {Alexander Van-Brunt},
journal= {arXiv preprint arXiv:1709.09561},
year = {2022}
}