The extremal ranks of \(A_1-B_1XC_1\) subject to a pair of matrix equations (Q879768)
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scientific article; zbMATH DE number 5151070
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The extremal ranks of \(A_1-B_1XC_1\) subject to a pair of matrix equations |
scientific article; zbMATH DE number 5151070 |
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The extremal ranks of \(A_1-B_1XC_1\) subject to a pair of matrix equations (English)
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9 May 2007
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Summary: For a given linear matrix expression \(A_1-B_1XC_1\), where \(X\) is a variable matrix, this paper gives two formulas for the maximal and minimal ranks of \(A_1-B_1XC_1\) subject to a pair of consistent matrix equations \(B_2XC_2=A_2\) and \(B_3XC_3=A_3\). As a consequence, we give necessary and sufficient conditions for the triple matrix equations \(B_1XC_1=A_1\), \(B_2XC_2=A_2\) and \(B_3XC_3=A_3\) to have a common solution.
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