Dual r-rank decomposition and its applications

• DOI: 10.1007/s40314-023-02490-9
• Publication Date: 2023-11-02T15:02:41Z
• Authors: Hongxing Wang; Chong Cui; Xiaoji Liu
• Keywords: 0203 mechanical engineering; Rings and Algebras (math.RA); 15A09; FOS: Mathematics; Mathematics - Rings and Algebras; 02 engineering and technology

In this paper, we introduce the dual $r$-rank decomposition of dual matrix, get its existence condition and equivalent form of the decomposition, as well as derive some characterizations of dual Moore-Penrose generalized inverse(DMPGI). Based on DMPGI, we introduce one special dual matrix(dual EP matrix). By applying the dual $r$-rank decomposition we derive several characterizations of dual EP matrix, dual idempotent matrix, dual generalized inverses, and the relationships among dual Penrose equations.