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Applying this factorization, we obtain an explicit representation of the group inverse in terms of four individual blocks of the partitioned matrix without certain restriction. We also derive some important coincidence theorems, including the expressions of the group inverse with Banachiewicz-Schur forms.<\/jats:p>","DOI":"10.1155\/2013\/247028","type":"journal-article","created":{"date-parts":[[2013,7,18]],"date-time":"2013-07-18T18:49:52Z","timestamp":1374173392000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["New Representations of the Group Inverse of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mn>2<\/mml:mn><mml:mo>\u00d7<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math>Block Matrices"],"prefix":"10.1155","volume":"2013","author":[{"given":"Xiaoji","family":"Liu","sequence":"first","affiliation":[{"name":"College of Science, Guangxi University for Nationalities, Nanning 530006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Science, Guangxi University for Nationalities, Nanning 530006, 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