Group invertible block matrices |
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| Authors: | Baodong Zheng Lizhu Sun Xiuwei Jiang |
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| Affiliation: | 1. School of Science, Harbin Institute of Technology, Harbin 150001, China2. College of Science, Harbin Engineering University, Harbin 150001, China |
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| Abstract: | Let M=(ABCD) (A and D are square) be a 2 × 2 block matrix over a skew field, where A is group invertible. Let S=D-CA#B denote the generalized Schur complement of M. We give the representations and the group invertibility of M under each of the following conditions:(1)S=0; (2) S is group invertible and CAπB=0, where Aπ=I-AA#. And the second result generalizes a result of C. Bu et al. [Appl. Math. Comput., 2009, 215: 132–139] |
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| Keywords: | Skew field group inverse generalized Schur complement block matrix |
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