Definite Matrix Polynomials and their Linearization by Definite Pencils

Definite Matrix Polynomials and their Linearization by Definite Pencils

Hyperbolic matrix polynomials are an important class of Hermitian matrix poly-nomials that contain overdamped quadratics as a special case. They share with definite pencils the spectral property that their eigenvalues are real and semisimple. We extend the definition of hyperbolic matrix polynomial in a way that relaxes the requirement of definiteness of the leading coefficient matrix, yielding...

Some new families of definite polynomials and the composition conjectures

The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

Notes on Hyperbolic Matrix Polynomials and Definite Linearizations

Max-plus Definite Matrix Closures and Their Eigenspaces

In this paper we introduce the definite closure operation for matrices with finite permanent, reveal inner structures of definite eigenspaces, and establish some facts about Hilbert distances between these inner structures and the boundary of the definite eigenspace.

Active Positive-Definite Matrix Completion

In the FindCandidates function (line 4), Select finds all the single edges that can be added to the current mask graph GΩ while maintaining its chordal structure. To do that, we make use of the clique tree data structure as introduced by Ibarra [1]. Given a graph G = (V,E), the clique tree is a tree C = (VC , EC), in which each node is a maximal clique of G, i.e., VC ⊂ 2 . In our case the numbe...