Similarity of the companion matrix and its transpose (with an appendix by Robert M. Guralnick)
type: Item
instance of: scholarly article
title: Similarity of the companion matrix and its transpose (with an appendix by Robert M. Guralnick)
zbMATH Open document ID: 0949.15016
DOI: 10.1016/S0024-3795(99)00210-4
author: Louis Solomon
published in: Linear Algebra and its Applications
publication date: 2000-12-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1419884
zbMATH Keywords: similarity
zbMATH Keywords: companion matrix
reviewed by: Witold Więsław
MaRDI profile type: Publication
cites work: Representations under ring extensions: Latimer-MacDuffee and Taussky correspondences
cites work: Noncommutative symmetric functions
cites work: Q5576154
cites work: A correspondence between classes of ideals and classes of matrices
cites work: On matrix classes corresponding to an ideal and its inverse
cites work: On the similarity transformation between a matrix and its transpose
description: scientific article; zbMATH DE number 1419884