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

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

Gravitational Scattering in the High-Energy Limit

Any gravitational scattering amplitude takes a remarkably simple factorized form at tree level in multi-Regge kinematics (MRK), where the produced particles are strongly ordered in rapidity. Very recently, it was shown that also the scattering equations have a very simple structure in MRK. In this paper we study Einstein gravity amplitudes in MRK in the framework of the scattering equations. We present a new derivation of the multi-Regge factorization of tree-level amplitudes with any number of external gravitons and any helicity configuration.Comment: 24 pages. v2: typos correcte

On the eigenvalues of a specially rank-r updated complex matrix

AbstractIn this paper, an alternatively simpler proof to an eigenvalue theorem of a specially structured rank-r updated complex matrix is presented and also its characteristic polynomial is explicitly determined by Leverrier’s algorithm for m–D system