2022•FilomatOpen access

Generalized inverses - idempotents and projectors

Zhimei Fu, Kezheng Zuo, Hui Yan, Honglin Zou, Yang Chen

Abstract

In this paper, we present necessary and sufficient conditions for X? to be idempotent and orthogonal idempotent, where X? ? {A?, AD, AD?, A?,D Aw}. Several characteristics when X? is idempotent and orthogonal idempotent are derived by core-EP decomposition. Additionally, we give some equivalent conditions when matrix A is orthogonal idempotent, using the properties of some generalized inverses of A.

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Key concepts: Idempotence, Mathematics, Idempotent matrix, Pure mathematics, Matrix (chemical analysis), Combinatorics, Algebra over a field, Materials science