Rank identities of commutator and Jordan product of scalar idempotent matrices independently of coefficients

摘要

The matrices P,Q is called the scalar idempotent matrices if P2=λP,Q2=μQ, where λ , μ are nonzero complexes. Started with the rank identities of general commutator and Jordan product of idempotent matrices, this paper obtains the ones for commutator and Jordan product of scalar idempotent matrices independently of λ, μ.