Similarity of the companion matrix and its transpose (with an appendix by Robert M. Guralnick) (Q1970458)
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scientific article; zbMATH DE number 1419884
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Similarity of the companion matrix and its transpose (with an appendix by Robert M. Guralnick) |
scientific article; zbMATH DE number 1419884 |
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Similarity of the companion matrix and its transpose (with an appendix by Robert M. Guralnick) (English)
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5 December 2000
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The author proves the following theorem: For any ring with unity the companion matrix \(C\) is similar to its transpose \(C^T\). Moreover, there exists an invertible symmetric matrix \(P\) with \(PCP^{-1}=C^T\). In an appendix to the paper Robert M. Guralnick gives another proof and some generalizations of the theorem.
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similarity
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companion matrix
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