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On the perturbation of weighted group inverse of rectangular matrices |
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| Authors: | Xiaoji Liu Zhaoliang Xu Qing Zhao Hui Wei |
| Affiliation: | 1. Faculty of Science, Guangxi University for Nationalities, Nanning, 530006, China 2. Guangxi Key Laboratory of Hybrid Computational and IC Design Analysis, Nanning, 530006, China 3. Department of Mathematics, Shanghai Maritime University, Shanghai, 200135, China 4. Suzhou Branch of China Construction Bank, Suzhou, China 5. Department of Computer Science, Fudan University, Shanghai, 200433, China |
| Abstract: | Cen (Math. Numer. Sin. 29:39–48, 2007) defined a weighted group inverse of rectangular matrices. For given matrices A∈C m×n and W∈C n×m , if X∈C m×n satisfies $$( W_{1} ) AWXWA=A, qquad ( W_{2} ) XWAWX=X,qquad ( W_{3} ) AWX=XWA $$ then X is called the W-weighted group inverse, which is denoted by $A_{W}^{#}$ . In this paper, for given rectangular matrices A and E and B=A+E, we investigate the perturbation of the weighted group inverse $A_{W}^{#}$ and present the upper bounds for $|B_{W}^{#} |$ . |
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