A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications (Q5948762)
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scientific article; zbMATH DE number 1671986
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications |
scientific article; zbMATH DE number 1671986 |
Statements
A representation of the general common solution to the matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) with applications (English)
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12 November 2001
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New necessary and sufficient conditions are derived for a pair of matrix equations \(A_1XB_1=C_1\) and \(A_2XB_2=C_2\) to have a common solution. Then a new representation is derived for the general common solution. The result is used to determine conditions for the existence of a solution and a new representation of the general Hermitian solution to the matrix equation \(AXB=C\) \((A,B\), and \(C\) are known matrices over the complex field).
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pair of matrix equations
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general common solution
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general Hermitian solution
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