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2013•Journal of Fuyang Teachers CollegeRequires access

Nonsingularity of linear combinations of idempotent matrices

Zeng Yue-d

Open publisher page 6 citations

Abstract

Idempotent matrix,a special type in matrix theory,possesses good properties and practical value.The sufficient and necessary conditions for nonsingularity of linear combinations of idempotent matrices were discussed by partitioned matrix.It was proved that A1 + A2 is nonsingular if and only if T is nonsingular,that A1-A2 is nonsingular if and only if T is nonsingular,and that M = NT-1H if and only if T and Ir-M are both,nonsingular.

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What this paper is about

Idempotent matrix,a special type in matrix theory,possesses good properties and practical value.The sufficient and necessary conditions for nonsingularity of linear combinations of idempotent matrices were discussed by partitioned matrix.It was proved that A1 + A2 is nonsingular if and only if T is nonsingular,that A1-A2 is nonsingular if and only if T is nonsingular,and that M = NT-1H if and only if T and Ir-M are both,nonsingular.

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Available abstract

Idempotent matrix,a special type in matrix theory,possesses good properties and practical value.The sufficient and necessary conditions for nonsingularity of linear combinations of idempotent matrices were discussed by partitioned matrix.It was proved that A1 + A2 is nonsingular if and only if T is nonsingular,that A1-A2 is nonsingular if and only if T is nonsingular,and that M = NT-1H if and only if T and Ir-M are both,nonsingular.

Key concepts: Invertible matrix, Idempotent matrix, Mathematics, Idempotence, Matrix (chemical analysis), Involutory matrix, Pure mathematics, Combinatorics

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