Extremal ranks of submatrices in an Hermitian solution to the matrix equation AXA *=B with applications |
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| Authors: | Yonghui Liu Yongge Tian |
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| Affiliation: | 1. Department of Applied Mathematics, Shanghai Finance University, Shanghai, 201209, People’s Republic of China
2. China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081, People’s Republic of China
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| Abstract: | Suppose that AXA *=B is a consistent matrix equation and partition its Hermitian solution X *=X into a 2-by-2 block form. In this paper, we give some formulas for the maximal and minimal ranks of the submatrices in an Hermitian solution X to AXA *=B. From these formulas we derive necessary and sufficient conditions for the submatrices to be zero or to be unique, respectively. As applications, we give some properties of Hermitian generalized inverses for an Hermitian matrix. |
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