On linear combinations of two idempotent matrices over an arbitrary field

Details On linear combinations of two idempotent matrices over an arbitrary field On linear combinations of two idempotent matrices over an arbitrary field

2009-07-25

arxiv.org/abs/0907.4436v2

Linear Algebra Appl. 433-3 (2010), 625-636

Mathematics

Rings and Algebras

18 pages (minor corrections)

Scientific paper

10.1016/j.laa.2010.03.023

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.

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