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On products of idempotent matrices

Published online by Cambridge University Press:  18 May 2009

J. A. Erdos
J. A. Erdos
Affiliation:
University of GlasgowGlasgow, W.2
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In [1], J. M. Howie considered the semigroup of transformations of sets and proved (Theorem 1) that every transformation of a finite set which is not a permutation can be written as a product of idempotents. In view of the analogy between the theories of transformations of finite sets and linear transformations of finite dimensional vector spaces, Howie's theorem suggests a corresponding result for matrices. The purpose of this note is to prove such a result.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 2 , July 1967 , pp. 118 - 122
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

1.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
2.van der Waerden, B. L., Modern algebra, Vol. II (New York, 1950).Google Scholar