2010•Journal of Hubei Normal UniversityRequires access

Idempotency of linear combinations of four idempotent matrices

Tao Xie

Abstract

Let P1,P2,P3,P4 be any four different nonzero mutually commutatiove idempotent matrices and c1,c2,c3,c4 be nonzero scalars.In the present note,some sufficient conditions for the matrix c1P1+c2P2+c3P3+c4P4 to be an idempotent matrix are given under the condition that the mutual product is zero or the mutual product is equal to the either one.

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Key concepts: Idempotence, Idempotent matrix, Mathematics, Product (mathematics), Matrix (chemical analysis), Combinatorics, Pure mathematics, Zero (linguistics)