Products of irreducible matrices |
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Authors: | Jia-yu Shao |
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Affiliation: | Department of Mathematics University of Wisconsin Madison Wisconsin 53706, USA |
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Abstract: | In this paper we characterize the subsemigroup of Bn (Bn is the multiplicative semigroup of n × n Boolean matrices) generated by all the irreducible matrices, and hence give a necessary and sufficient condition for a Boolean matrix A to be a product of irreducible Boolean matrices. We also give a necessary and sufficient condition for an n × n nonnegative matrix to be a product of nonnegative irreducible matrices. |
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