On determinantal representation for the generalized inverse A and its applications |
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| Authors: | Jing Cai Guoliang Chen |
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| Affiliation: | 1. School of Science, Huzhou Teachers College, Huzhou 313000, ChinaSchool of Science, Huzhou Teachers College, Huzhou 313000, China===;2. Department of Mathematics, East China Normal University, Shanghai 200062, China |
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| Abstract: | In this paper, first we establish a determinantal representation for the group inverse Ag of a square matrix A. Based on this, a determinantal representation for the generalized inverse A is presented. As an application, we give a determinantal formula for the unique solution of the general restricted linear system: Ax=b(x ∈ T, b ∈ AT and dim(AT)=dim(T)), which reduces to the common Cramer rule if A is non‐singular. These results extend our earlier work. Copyright © 2006 John Wiley & Sons, Ltd. |
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| Keywords: | determinantal representation group inverse compound matrix restricted linear system |
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