Graphical criteria for positive solutions to linear systems

Meritxell Sáez, Elisenda Feliu, Carsten Wiuf

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We study linear systems of equations with coefficients in a generic partially ordered ring R and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two nonnegative elements in R. The requirement of a nonnegative solution arises typically in applications, for example in biology and ecology, where quantities of interest are concentrations and abundances. We provide novel conditions on a labeled multidigraph associated with the linear system that guarantee the solution to be nonnegative. Furthermore, we study a generalization of the first class of linear systems, where the coefficient matrix has a specific block form and provide analogous conditions for nonnegativity of the solution, similarly based on a labeled multidigraph. The latter scenario arises naturally in chemical reaction network theory, when studying full or partial parameterizations of the positive part of the steady state variety of a polynomial dynamical system in the concentrations of the molecular species.

Idioma originalAnglès
Pàgines (de-a)166-193
Nombre de pàgines28
RevistaLinear Algebra and Its Applications
Estat de la publicacióPublicada - 1 de set. 2018
Publicat externament


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