The matrix equation \(XA-BX=R\) and its applications (Q1109847)
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scientific article; zbMATH DE number 4071107
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The matrix equation \(XA-BX=R\) and its applications |
scientific article; zbMATH DE number 4071107 |
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The matrix equation \(XA-BX=R\) and its applications (English)
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1988
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The author considers the Sylvester equation \(XA-BX=R\) for X where A, B and R are \(n\times n\) complex matrices, and B is nonderogatory. The main theorem shows that if only the first n-1 rows of R are given, then there is at most one solution X with a specified first row, and the author characterizes the case where X is nonsingular. This result is used to construct symmetrizers and commuting matrices, to compute the number of common eigenvalues between A and B, and to reprove some results on symmetrizers, Bézoutians and inertia.
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matrix equation
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Sylvester equation
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symmetrizers
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commuting matrices
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common eigenvalues
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Bézoutians
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inertia
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