Note on a Theorem on Singular Matrices

Abstract

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).