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2008•Journal of Hubei Normal UniversityRequires access

Everymatrix is a sum of two rank-idempotent matrices

Kezheng Zuo

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Abstract

This paper researches some properties of rank-idempotent matrix,and the linear combinations' structures of two rank-idempotent matrices.By using the generalized inverse of matrix,the Jordan canonical form of matrix and the rational canonical form of matrix,we get some new characters of rank-idempotent matrix,and prove that every matrix is a sum of two rank-idempotent matrices.

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What this paper is about

This paper researches some properties of rank-idempotent matrix,and the linear combinations' structures of two rank-idempotent matrices.By using the generalized inverse of matrix,the Jordan canonical form of matrix and the rational canonical form of matrix,we get some new characters of rank-idempotent matrix,and prove that every matrix is a sum of two rank-idempotent matrices.

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Available abstract

This paper researches some properties of rank-idempotent matrix,and the linear combinations' structures of two rank-idempotent matrices.By using the generalized inverse of matrix,the Jordan canonical form of matrix and the rational canonical form of matrix,we get some new characters of rank-idempotent matrix,and prove that every matrix is a sum of two rank-idempotent matrices.

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

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