Further characterizations of the weak group inverse of matrices and the weak group matrix

• Main Authors: Hui Yan, Hongxing Wang, Kezheng Zuo, Yang Chen
• Format: Article
• Language: English
• Published: AIMS Press 2021-06-01
• Series: AIMS Mathematics
• Subjects: weak group inverse; weak group matrix; core-ep decomposition; rang space; null space
• Online Access: https://www.aimspress.com/article/doi/10.3934/math.2021542?viewType=HTML
• ISSN: 2473-6988

This paper is devoted to consider some new characteristics and properties of the weak group inverse and the weak group matrix. First, we characterize the weak group inverse of a square matrix based on its range space and null space. Also several different characterizations of the weak group inverse are presented by projection and the Bott-Duffin inverse. Then by using the core-EP decomposition, we investigate the relationships between weak group inverse and other generalized inverses. And some new characterizations of weak group matrix are obtained.