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Soft Computing
Published in: Soft Computing 17/2019

14-01-2019 | Foundations

The solvable conditions of linear system over commutative semirings

Authors: Qian-yu Shu, Xue-ping Wang

Published in: Soft Computing | Issue 17/2019

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Abstract

This paper deals with the solution of linear system over commutative semirings. It uses the bideterminant of a matrix to investigate the solvable conditions of a system of linear equations and gives some necessary and sufficient conditions that a system of linear equations is solvable.
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Literature
Gondran M, Minoux M (2008) Graphs, dioids and semirings. Springer, New YorkMATH
Kuntzman J (1972) Théorie des réseaaux graphes [Theory of network graphs]. Dunod (Libraire), Paris
McDonald BR (1984) Linear algebra over commutative rings. Marcel Dekker, New YorkMATH
Perfilieva I, Kupka J (2010) Kronecker-capelli theorem in semilinear spaces. In: Ruan D, Li TR, Xu Y, Chen GQ, Kerre EE (eds) Computational intelligence: foundations and applications. World Scientific, Emei, pp 43–51CrossRef
Shu Q, Wang X (2017) The applications of the bideterminant of a matrix over commutative semirings. Linear Multilinear Algebra 65:1462–1478MathSciNetCrossRefMATH
Wang X, Shu Q (2014) Bideterminant and rank of matrix. Soft Comput 18:729–742CrossRef
Zimmermann U (1981) Linear and combinatorial optimization in ordered algebraic structures, annals of discrete mathematics, vol 10. North Holland, Amsterdam
Metadata
Title
The solvable conditions of linear system over commutative semirings
Authors
Qian-yu Shu
Xue-ping Wang
Publication date
14-01-2019
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 17/2019
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-019-03758-1

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