Ranks of Solutions of the Matrix Equation AXB = C |
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| Authors: | Yongge Tian |
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| Institution: | Department of Mathematics and Statistics , Queen's University Kingston , Ontario , Canada , K7L 3N6 |
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| Abstract: | The purpose of this article is to solve two problems related to solutions of a consistent complex matrix equation AXB = C : (I) the maximal and minimal ranks of solution to AXB = C , and (II) the maximal and minimal ranks of two real matrices X 0 and X 1 in solution X = X 0 + iX 1 to AXB = C . As applications, the maximal and minimal ranks of two real matrices C and D in generalized inverse (A + iB)- = C + iD of a complex matrix A + iB are also examined. |
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| Keywords: | Block Matrix Generalized Inverse Matrix Equation Rank Solution |
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