Combinatorics Seminar 2015

Date: Wed, May 20, 2015

Time: 15:00 - 16:00

Venue: Middle Meeting Room

Title: On matrix $D$-stability and related properties

Abstract:

We study the positive stability and $D$-stability of $P$-matrices. We also consider the property of $D_{\theta}$-stability, i.e. when a matrix remains positive stable being multiplied by a positive diagonal matrix from a special class. This class is defined by a given permutation $\theta$. We apply the obtained results to some problems connected with structured matrices. Namely, we study $M$-matrices and their rank one perturbations. With the help of the obtained results we introduce new classes of $D$-stable matrices and provide the proof for the still open conjecture of Bierkens--Ran concerning rank one perturbations of singular $M$-matrices.

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