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Every matrix is a linear combination of three idempotents

✍ Scribed by Vyacheslav Rabanovich

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 173 KB
Volume: 390
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.04.014

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✦ Synopsis

It is shown that every n × n matrix over a field of characteristic zero is a linear combination of three idempotent matrices. It is proved that both 2 × 2 matrices and complex 3 × 3 matrices are linear combinations of two idempotents. Also we present 3 × 3 and 4 × 4 matrices that are not linear combinations of any two idempotents.

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