2014•Journal of Anhui University of TechnologyRequires access

Studies of Similar Idempotent Matrix and its Properties

Shen Shiha

Abstract

By defing matrix A as B-similar idempotent if it satisfies the condition of A2=BAa generalization of idempotent matrix was investigated. The conditions of diagonalization of similar idempotent matrices on complex field was characterized, and the method on how to decompose a matrix on complex field into similar idempotent matrices was discussed. Moreover, the Jordan form and the rank of similar idempotent matrices was studied, and some inequalities of matrix rank as well as the forms of Jordan decompositions of similar idempotent matrices were obtained. As a result, some well-known results on idempotent matrix in matrix theory were generalized.

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