期刊
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
卷 31, 期 2, 页码 732-754出版社
SIAM PUBLICATIONS
DOI: 10.1137/080718838
关键词
sign patterns; signed matrices; determinants of Jacobians; chemical reaction networks
资金
- NSF [DMS-0700758, DMS-0757212]
- Ford Motor Co.
- Slovenian Research Agency [Z1-9570-0101-06]
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.
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