Some properties of submatrices in a solution to the matrix equation AXB=C with applications |
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| Authors: | Yongge Tian |
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| Institution: | China Economics and Management Academy, Central University of Finance and Economics, Beijing, China |
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| Abstract: | Suppose that AXB=C is a consistent matrix equation and partition its solution X into a 2×2 block form. In this article we give some formulas for the maximal and minimal ranks of the submatrices in a solution X to AXB=C. From these formulas, we derive necessary and sufficient conditions for the submatrices to be zero and nonsingular, respectively. As applications, we give a group of formulas for the maximal and minimal ranks of submatrices in generalized inverses of matrices and their properties. |
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| Keywords: | primary 15A24 secondary 15A03 15A09 |
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