English

On linear combinations of two idempotent matrices over an arbitrary field

Rings and Algebras 2010-05-14 v2

Abstract

Given an arbitrary field K and non-zero scalars a and b, we give necessary and sufficient conditions for a matrix A in M_n(K) to be a linear combination of two idempotents with coefficients a and b. This extends results previously obtained by Hartwig and Putcha in two ways: the field K considered here is arbitrary (possibly of characteristic 2), and the case a is different from b and -b is taken into account.

Keywords

Cite

@article{arxiv.0907.4436,
  title  = {On linear combinations of two idempotent matrices over an arbitrary field},
  author = {Clément de Seguins Pazzis},
  journal= {arXiv preprint arXiv:0907.4436},
  year   = {2010}
}

Comments

18 pages (minor corrections)

R2 v1 2026-06-21T13:28:59.864Z