Basis-free solution to general linear quaternionic equation

DOI10.1080/03081087.2018.1508404zbMath1448.15018arXiv1707.00685OpenAlexW2964004579WikidataQ114641421 ScholiaQ114641421MaRDI QIDQ5217483

Lei Huang, Changpeng Shao, Hong-Bo Li

Publication date: 24 February 2020

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.00685

zbMATH Keywords

Clifford algebraSylvester equationbasis-free solutionlinear quaternionic equation

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Clifford algebras, spinors (15A66) Computational aspects of associative rings (general theory) (16Z05) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (3)

Conformal group theory of tensor structures ⋮ Numerical solution of singular Sylvester equations ⋮ Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension

Cites Work

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• The quaternionic equation \(ax + xb = c\)
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• Algorithms for quaternion polynomial root-finding
• THE QUATERNIONIC DIRAC LAGRANGIAN
• A Note on the Computation of All Zeros of Simple Quaternionic Polynomials
• On the Structure of the Set of Zeros of Quaternionic Polynomials
• Equations in Quaternions
• On the equation 𝜒𝛼=𝛾𝜒+𝛽 over an algebraic division ring
• The “fundamental theorem of algebra” for quaternions
• Computing the zeros of quaternion polynomials.

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