{"title":"Weak CMP inverses","authors":"Dijana Mosić","doi":"10.1007/s00010-025-01167-4","DOIUrl":null,"url":null,"abstract":"<div><p>We consider extended systems of matrix equations than well-known systems for presenting the CMP inverse in terms of a minimal rank weak Drazin inverse and minimal rank right weak Drazin inverse. Solutions of new extended systems present new kinds of generalized inverses and they are called a weak CMP inverse and a right weak CMP inverse. Beside that the CMP, MPCEP and *CEPMP inverses are special types of weak CMP and right weak CMP inverses, we study two particular classes of weak CMP inverse which are new in literature. A number of characterizations and representations for weak CMP inverse are developed. Perturbation formulae and perturbation bounds for weak CMP inverse are proved. Applications of the weak CMP inverse for solving linear equations are presented. Consequently, we obtain the classical result about application of the Moore–Penrose inverse in solving linear equation.</p></div>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":"99 4","pages":"1705 - 1724"},"PeriodicalIF":0.7000,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00010-025-01167-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider extended systems of matrix equations than well-known systems for presenting the CMP inverse in terms of a minimal rank weak Drazin inverse and minimal rank right weak Drazin inverse. Solutions of new extended systems present new kinds of generalized inverses and they are called a weak CMP inverse and a right weak CMP inverse. Beside that the CMP, MPCEP and *CEPMP inverses are special types of weak CMP and right weak CMP inverses, we study two particular classes of weak CMP inverse which are new in literature. A number of characterizations and representations for weak CMP inverse are developed. Perturbation formulae and perturbation bounds for weak CMP inverse are proved. Applications of the weak CMP inverse for solving linear equations are presented. Consequently, we obtain the classical result about application of the Moore–Penrose inverse in solving linear equation.
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
