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On decomposing any matrix as a linear combination of three idempotents

✍ Scribed by Clément de Seguins Pazzis


Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
183 KB
Volume
433
Category
Article
ISSN
0024-3795

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Every matrix is a linear combination of
✍ Vyacheslav Rabanovich 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 173 KB

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 comb