Invertible matrices and semilinear spaces over commutative semirings

Authors:
Shan Zhao;Xue-ping Wang
Affiliations:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China;College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

This paper deals with invertible matrices and semilinear spaces over commutative semirings. Some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained. The condition under which the cardinality of each basis of semilinear space of n-dimensional vectors is n is given. In the end, the factor rank of matrices over semirings is investigated.