The relation between the companion matrix and the companion polynomial in \(\mathbb {R}^4\) algebras
type: Item
instance of: scholarly article
title: The relation between the companion matrix and the companion polynomial in \(\mathbb {R}^4\) algebras
zbMATH Open document ID: 1431.15016
author: Drahoslava Janovská
author: Gerhard Opfer
published in: Advances in Applied Clifford Algebras
publication date: 2018-10-26T00:00:00Z
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 12D10
zbMATH DE Number: 6966024
zbMATH Keywords: quaternionic companion matrix
zbMATH Keywords: quaternionic companion polynomial
zbMATH Keywords: characteristic polynomial of quaternionic companion matrix
zbMATH Keywords: coquaternionic companion matrix
zbMATH Keywords: coquaternionic companion polynomial
zbMATH Keywords: characteristic polynomial of coquaternionic companion matrix
MaRDI profile type: Publication
full work available at URL: s00006-018-0892-5
OpenAlex ID: W2884493449
cites work: Matrices of quaternions
cites work: On eigenvalues of split quaternion matrices
cites work: On the eigenvalues of quaternion matrices
cites work: Q3016260
cites work: On the Zeros of Polynomials over Division Rings
cites work: Q4382291
cites work: Q3998992
cites work: The number of zeros of unilateral polynomials over coquaternions and related algebras
cites work: Matrices over nondivision algebras without eigenvalues
cites work: Zeros and singular points for one-sided coquaternionic polynomials with an extension to other \(R^4\) algebras
cites work: A Note on the Computation of All Zeros of Simple Quaternionic Polynomials
cites work: Q5675788
cites work: Q5794701
cites work: Equations in Quaternions
cites work: Niven's algorithm applied to the roots of the companion polynomial over \(\mathbb {R}^4\) algebras
cites work: On the eigenvalues and eigenvectors of a Lorentzian rotation matrix by using split quaternions
cites work: Q5173760
cites work: Computing the zeros of quaternion polynomials.
cites work: Q3259734
cites work: Quaternions and matrices of quaternions
DOI: 10.1007/S00006-018-0892-5
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description: scientific article; zbMATH DE number 6966024