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2011•Journal of Shanxi Datong UniversityRequires access

The Necessary and Sufficient Conditions for Idempotent Matrix and Rank-idempotent Matrix

He Mei

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Abstract

A matrix of satisfying A= A2 is called idempotent matrix.It is an idempotent element of matrix ring Mn(F).A matrix of satisfying r(A)= r(A2) is called rank-idempotent matrix.They are closely related to decomposition of space and invariant subspace.Some properties of idempotent matrix and rank-idempotent matrix are discussed by using methods of linear space.The necessary and sufficient conditions for idempotent matrix and rank-idempotent matrix are given.

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What this paper is about

A matrix of satisfying A= A2 is called idempotent matrix.It is an idempotent element of matrix ring Mn(F).A matrix of satisfying r(A)= r(A2) is called rank-idempotent matrix.They are closely related to decomposition of space and invariant subspace.Some properties of idempotent matrix and rank-idempotent matrix are discussed by using methods of linear space.The necessary and sufficient conditions for idempotent matrix and rank-idempotent matrix are given.

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Available abstract

A matrix of satisfying A= A2 is called idempotent matrix.It is an idempotent element of matrix ring Mn(F).A matrix of satisfying r(A)= r(A2) is called rank-idempotent matrix.They are closely related to decomposition of space and invariant subspace.Some properties of idempotent matrix and rank-idempotent matrix are discussed by using methods of linear space.The necessary and sufficient conditions for idempotent matrix and rank-idempotent matrix are given.

Key concepts: Idempotent matrix, Square root of a 2 by 2 matrix, Mathematics, Matrix ring, Idempotence, Involutory matrix, Rank (graph theory), Matrix (chemical analysis)

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