2012•Journal of Qufu Normal UniversityRequires access

Study on Necessary and Sufficient Conditions for Idempotent Matrix

Xiaoli Song

Abstract

The concept of(m,l) idempotent matrices is an integration of m idempotent matrices and m unit-potent matrices.In this paper,a new necessary and sufficient condition to discriminate(m,l) idempotent matrices by using an equation associated with ranks of series matrices,which related to unit roots is given,the similar canonical form of(m,l) idempotent matrices is presented,and a formula for the trace of a matrix expressed in rank of matrices is obtained.

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