On decomposing any matrix as a linear combination of three idempotents
arXiv:0907.4949 · doi:10.1016/j.laa.2010.04.017
Abstract
In a recent article, we gave a full characterization of matrices that can be decomposed as a linear combination of two idempotents with prescribed coefficients. In this one, we use those results to improve on a recent theorem of V. Rabanovich: we establish that every square matrix is a linear combination of three idempotents (for an arbitrary coefficient field rather than just a field of characteristic 0).
arXiv comment20 pages, simplified proofs, new references added