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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2013
- arXiv:
- arXiv:1312.2491
- Bibcode:
- 2013arXiv1312.2491B
- Keywords:
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- Mathematics - Rings and Algebras;
- Mathematics - Numerical Analysis;
- 15A18;
- 15BXX;
- 34D20
- E-Print:
- Linear Algebra and its Applications Volume 457, 15 September 2014, Pages 191-208