Abstract
Necessary and sufficient conditions are derived for a 2-by-2 partitioned matrix to have {1}-, {1,2}-, {1,3}-, {1,4}-inverses and the Moore–Penrose inverse with Banachiewicz–Schur forms. As applications, the Banachiewicz–Schur forms of {1}-, {1,2}-, {1,3}-, {1,4}-inverses and the Moore–Penrose inverse of a 2-by-2 partitioned Hermitian matrix are also given.
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