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Note on a Theorem on Singular Matrices

Published online by Cambridge University Press:  20 November 2018

D. Ž. Djoković
D. Ž. Djoković*
Affiliation:
University of Waterloo
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J. A. Erdös proved recently [1] that every singular matrix over a field F is a product of idempotent matrices. He gave two proofs, one valid for matrices which are similar to triangular matrices and the other valid in general. We shall give a simple geometric proof of the above result. Instead of matrices we use linear operators. Moreover we get an explicit factorization in terms of projectors (idempotent operators).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 283 - 284
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Erdös, J. A., On products of idempotent matrices. Glasgow Math. J. 8(1967) 118-122.Google Scholar
2. Gantmacher, F.R., The theory of matrices. Vol. 1. (Chelsea Publishing Company, New York 1960).Google Scholar