DETERMINANT EXPANSIONS OF SIGNED MATRICES AND OF CERTAIN JACOBIANS

被引：13

作者：

Helton, J. William ^{[1
]}

Klep, Igor ^{[2
]}

Gomez, Raul ^{[1
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ Ljubljana, IMFM, SI-11111 Ljubljana, Slovenia

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2009年 / 31卷 / 02期

关键词：

sign patterns; signed matrices; determinants of Jacobians; chemical reaction networks; CHEMICAL-REACTION NETWORKS; MULTIPLE EQUILIBRIA; CRITERION; STABILITY; PATTERNS; SYSTEMS;

D O I：

10.1137/080718838

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper treats two topics: Matrices with sign patterns and Jacobians of certain mappings on the nonnegative orthant R(>= 0)(d). The main topic is counting the number of positive and negative 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 [SIAM J. Appl. Math., 65 (2005), pp. 1526-1546; SIAM J. Appl. Math., 66 (2006), pp. 1321-1338]. We also give a graph-theoretic test for determining when the sign pattern of the Jacobian of a chemical reaction dynamics is unambiguous.

引用

页码：732 / 754

页数：23

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