2010•Journal of Baoji University of Arts and SciencesRequires access

Some studies about linear combinations of three idempotent matrices

Tao Xie

Abstract

Aim To study some conditions when the matrix c1P1+c2P2+c3P3 is an idempotent matrix where P1,P2 and P3 are any three nonzero mutually commutative n×n idempotent matrices and c1,c2 and c3 are nonzero scalars.Methods The induction method is used to find the results.Results Some sufficient conditions for the matrix c1P1+c2P2+c3P3 to be an idempotent matrix are given and a necessary and sufficient condition for the matrix P1+P2+P3 is given too.Conclusion The results furnish the related theory of linear combinations of idempotent matrices.

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Key concepts: Idempotent matrix, Idempotence, Mathematics, Matrix (chemical analysis), Square root of a 2 by 2 matrix, Pure mathematics, Commutative property, Involutory matrix