Geodesic
Note on a Theorem on Singular Matrices
Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 283-284

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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). 
Djoković, D. Ž. Note on a Theorem on Singular Matrices. Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 283-284. doi: 10.4153/CMB-1968-034-9
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     title = {Note on a {Theorem} on {Singular} {Matrices}},
     journal = {Canadian mathematical bulletin},
     pages = {283--284},
     year = {1968},
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     number = {2},
     doi = {10.4153/CMB-1968-034-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-034-9/}
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