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Determinant Expansions of Signed Matrices and of Certain Jacobians

Research paper by J. William Helton, Igor Klep, Raul Gomez

Indexed on: 28 Feb '08Published on: 28 Feb '08Published in: Mathematics - Rings and Algebras



Abstract

This paper treats two topics: matrices with sign patterns and Jacobians of certain mappings. The main topic is counting the number of plus and minus coefficients in the determinant expansion of sign patterns and of these Jacobians. The paper is motivated by an approach to chemical networks initiated by Craciun and Feinberg. We also give a graph-theoretic test for determining when the Jacobian of a chemical reaction dynamics has a sign pattern.