A singular M-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it D-stable?

A.C.M. Ran; J. Bierkens

doi:10.1016/j.laa.2014.05.022

A singular M-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it D-stable?

A.C.M. Ran, J. Bierkens

Mathematics

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Abstract

The positive stability and D-stability of singular M-matrices, perturbed by (non-trivial) nonnegative rank one perturbations, is investigated. In special cases positive stability or D-stability can be established. In full generality this is not the case, as illustrated by a counterexample. However, matrices of the mentioned form are shown to be P-matrices. © 2014 Elsevier Inc.

Original language	English
Pages (from-to)	191-208
Journal	Linear Algebra and its Applications
Volume	457
DOIs	https://doi.org/10.1016/j.laa.2014.05.022
Publication status	Published - 2014

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10.1016/j.laa.2014.05.022

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@article{e13a2b869c2b487aa9fe795d66d82786,

title = "A singular M-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it D-stable?",

abstract = "The positive stability and D-stability of singular M-matrices, perturbed by (non-trivial) nonnegative rank one perturbations, is investigated. In special cases positive stability or D-stability can be established. In full generality this is not the case, as illustrated by a counterexample. However, matrices of the mentioned form are shown to be P-matrices. {\textcopyright} 2014 Elsevier Inc.",

author = "A.C.M. Ran and J. Bierkens",

year = "2014",

doi = "10.1016/j.laa.2014.05.022",

language = "English",

volume = "457",

pages = "191--208",

journal = "Linear Algebra and its Applications",