The least squares g-inverses for sum of matrices |
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| Authors: | Zhiping Xiong Yingying Qin Bing Zheng |
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| Institution: | 1. Department of Mathematics , Wuyi University , Jiangmen 529020 , P.R. China xzpwhere@163.com;3. Department of Mathematics , Wuyi University , Jiangmen 529020 , P.R. China;4. School of Mathematics and Statistics , Lanzhou University , Lanzhou 730000 , P.R. China |
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| Abstract: | In this article, we exhibit under suitable conditions a neat relationship between the least squares g-inverse for a sum of two matrices and the least squares g-inverses of the individual terms. We give a necessary and sufficient condition for the set equations (A?+?B){1,?3}?=?A{1,?3}?+?B{1,?3} and (A?+?B){1,?4}?=?A{1,?4}?+?B{1,?4}. |
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| Keywords: | the least squares g-inverse the minimum norm g-inverse maximal rank minimal rank generalized parallel sum |
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