Cauchy-type determinants and integrable systems (Q975611)
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scientific article; zbMATH DE number 5719628
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cauchy-type determinants and integrable systems |
scientific article; zbMATH DE number 5719628 |
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Cauchy-type determinants and integrable systems (English)
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10 June 2010
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It is well known that the Sylvester matrix equation \(AX+XB=C\) has a unique solution \(X\) if and only if \(0\notin \text{spec}(A) + \text{spec}(B)\). In the present article explicit formulas for the determinant of \(X\) are given, in the case the \(C\) is one-dimensional. For diagonal matrices \(A, B\), a classical result by Cauchy is obtained as a special case.
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Cauchy-type determinants
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Sylvester matrix equation
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integrable systems
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multiple pole solutions
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