Geodesic
On products of idempotent matrices
Glasgow mathematical journal, Tome 8 (1967) no. 2, pp. 118-122

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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. 
Erdos, J. A. On products of idempotent matrices. Glasgow mathematical journal, Tome 8 (1967) no. 2, pp. 118-122. doi: 10.1017/S0017089500000173
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[1] 1.Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, London Math. Soc. 41 (1966), 707–716. Google Scholar | DOI

[2] 2.van der Waerden, B. L., Modern algebra, Vol. II (New York, 1950). Google Scholar

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