Similarity of the companion matrix and its transpose (with an appendix by Robert M. Guralnick) (Q1970458)

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.