On similarity of matrices over commutative rings
type: Item
instance of: scholarly article
title: On similarity of matrices over commutative rings
zbMATH Open document ID: 1073.15009
published in: Linear Algebra and its Applications
publication date: 2005-04-21T00:00:00Z
review text: Let \(R\) be a commutative ring and let \(A\) be an \(n\times n\) matrix over \(R\). The author gives some direct criteria that determine when \(A\) is similar to its companion matrix or to a diagonal matrix over \(R\). He also gives conditions for the existence of a factorization \(A(x)= (xI_n- B)C(x)\) in the matrix ring \(R_{n,n}[x]\), \(x\) an indeterminant.
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 2160190
zbMATH Keywords: matrix similarity
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: companion matrix
zbMATH Keywords: diagonal matrix
zbMATH Keywords: factorization
author: V. M. Prokip
MaRDI profile type: Publication
full work available at URL: j.laa.2004.11.015
OpenAlex ID: W1964909950
cites work: Q3315642
cites work: Diagonalization Over Commutative Rings
cites work: Simultaneous diagonalization of an algebraic family of matrices
cites work: Q4029570
cites work: Diagonalization of matrices over regular rings
cites work: Simultaneous reduction to triangular forms after extension with zeroes
cites work: Q5523899
cites work: Q5668937
cites work: Equivalence of partitioned matrices
DOI: 10.1016/J.LAA.2004.11.015
description: scientific article; zbMATH DE number 2160190