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arXiv · 0907.4949

On decomposing any matrix as a linear combination of three idempotents

Clément de Seguins Pazzis
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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).

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Clément de Seguins Pazzis. 2009-07-28. On decomposing any matrix as a linear combination of three idempotents. https://doi.org/10.1016/j.laa.2010.04.017

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