On decomposing any matrix as a linear combination of three idempotents

Details On decomposing any matrix as a linear combination of three idempotents On decomposing any matrix as a linear combination of three idempotents

2009-07-28

arxiv.org/abs/0907.4949v2

Linear Algebra Appl. 433-4 (2010), 843-855

Mathematics

Rings and Algebras

20 pages, simplified proofs, new references added

Scientific paper

10.1016/j.laa.2010.04.017

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).

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