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On decomposing any matrix as a linear combination of three idempotents

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
433
Issue
4
Identifiers
DOI: 10.1016/j.laa.2010.04.017
Keywords
  • Matrices
  • Idempotents
  • Linear Combination
  • Decomposition
  • Cyclic Matrices
Disciplines
  • Mathematics

Abstract

Abstract In a recent article, we gave a full characterization of matrices that can be decomposed as linear combinations of two idempotents with prescribed coefficients. In this one, we use those results to improve on a recent theorem of Rabanovich: we establish that every square matrix is a linear combination of three idempotents (for an arbitrary coefficient field rather than just one of characteristic 0).

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