Determinant Expansions of Signed Matrices and of Certain Jacobians

Details Determinant Expansions of Signed Matrices and of Certain Jacobians Determinant Expansions of Signed Matrices and of Certain Jacobians

2008-02-29

arxiv.org/abs/0802.4319v1

SIAM J. Matrix Anal. Appl. 31 (2009), no. 2, 732-754

Mathematics

Rings and Algebras

25 pages

Scientific paper

10.1137/080718838

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.

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