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arXiv · 1312.2491

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

Joris Bierkens·André Ran
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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.

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Joris Bierkens, André Ran. 2014-05-09. A singular M-matrix perturbed by a nonnegative rank one matrix has positive principal minors; is it D-stable?. https://doi.org/10.1016/j.laa.2014.05.022

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