On sums of idempotent matrices over a field of positive characteristic

Abstract

We study which matrices are sums of idempotents over a field of non-zero characteristic; in particular, we prove that any such matrix, provided it is large enough, is actually a sum of five idempotents, and even of four when the field is a prime one.

arXiv comment16 pages, minor corrections from the first version

References in corpus (2)

• On decomposing any matrix as a linear combination of three idempotents
• On linear combinations of two idempotent matrices over an arbitrary field

Cited by in corpus (1)

• Twists of two or multiple idempotent matrices