{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:02Z","timestamp":1760240222864,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T00:00:00Z","timestamp":1555286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let A be an     n \u00d7 n     complex matrix. The     ( B , C )    -inverse     A  \u2225 ( B , C )      of A was introduced by Drazin in 2012. For given matrices A and B, several rank equalities related to     A  \u2225 (  B 1  ,  C 1  )      and     B  \u2225 (  B 2  ,  C 2  )      of A and B are presented. As applications, several rank equalities related to the inverse along an element, the Moore-Penrose inverse, the Drazin inverse, the group inverse and the core inverse are obtained.<\/jats:p>","DOI":"10.3390\/sym11040539","type":"journal-article","created":{"date-parts":[[2019,4,15]],"date-time":"2019-04-15T11:15:58Z","timestamp":1555326958000},"page":"539","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Rank Equalities Related to the Generalized Inverses A\u2016(B1,C1), D\u2016(B2,C2) of Two Matrices A and D"],"prefix":"10.3390","volume":"11","author":[{"given":"Wenjie","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9744-477X","authenticated-orcid":false,"given":"Sanzhang","family":"Xu","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3222-3036","authenticated-orcid":false,"given":"Julio","family":"Ben\u00edtez","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica Multidisciplinar, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,15]]},"reference":[{"key":"ref_1","first-page":"394","article-title":"On the reciprocal of the general algebraic matrix","volume":"26","author":"Moore","year":"1920","journal-title":"Bull. 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