2025/08/06 by Yukun Zhou, Jianlong Chen, Zhou, Yukun +3 · 1 citation
Computer Science · #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2508.04363
openalex publication_date 2025/08/06 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
Let a,~f be elements in a ring with pseudo core inverses a^\scriptsize\textcircled\tiny D, f^\scriptsize\textcircled\tiny D, and let b=f-a. We prove that the absorption law a^\scriptsize\textcircled\tiny D(a+f)f^\scriptsize\textcircled\tiny D=a^\scriptsize\textcircled\tiny D+f^\scriptsize\textcircled\tiny D holds if and only if 1+a^\scriptsize\textcircled\tiny Db is invertible and the additive property f^\scriptsize\textcircled\tiny D=(1+a^\scriptsize\textcircled\tiny Db)-1a^\scriptsize\textcircled\tiny D is satisfied. We further characterize these properties and establish analogous results for other generalized inverses. Finally, we apply these results to the case of complex matrices.