On the solvability of the Sylvester equation (Q1365713)
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scientific article; zbMATH DE number 1058644
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solvability of the Sylvester equation |
scientific article; zbMATH DE number 1058644 |
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On the solvability of the Sylvester equation (English)
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21 July 1998
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This paper revisits the classical Sylvester equation: \(AH- HD=P\) where \(A,D\) and \(P\) are \(n\times n\) matrices. It addresses the issues on the existence of an invertible solution \(H\) in the Sylvester equation. It presents necessary and sufficient conditions for the existence of a solution when the matrices \(A\) and \(D\) are cyclic and the matrix \(P\) is of rank 1. Its applications to control theory on controllability and observability are also noted. This paper adds new results to a classical problem.
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solvability
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cyclic matrices
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operator algebra
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Sylvester equation
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controllability
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observability
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0.7905081510543823
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0.7883431315422058
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0.7822737097740173
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