Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)

descriptionPublicationkeyboard_double_arrow_right Article 20 Feb 2021 English Publisher:WileyJournal:Mathematical Methods in the Applied Sciences, volume 46, pages 15,952-15,971 (issn: 0170-4214, eissn: 1099-1476,

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Authors: Ming‐Zhao Li; Shi‐Fang Yuan; Hua Jiang;

doi: 10.1002/mma.7273

Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)

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Abstract

This paper provides two direct methods for solving the split quaternion matrix equation whereXis an unknown split quaternionη‐Hermitian matrix, andA, B, C, D, E, Fare known split quaternion matrices with suitable size. Our tools are the Kronecker product, Moore–Penrose generalized inverse, real representation, and complex representation of split quaternion matrices. Our main work is to find the necessary and sufficient conditions for the existence of a solution of the matrix equation mentioned above, derive the explicit solution representation, and provide four numerical algorithms and two numerical examples.

Related Organizations

Wuyi University
China (People's Republic of)
Wuyi University
China (People's Republic of)

Keywords

matrix equation, Kronecker product, Matrices over special rings (quaternions, finite fields, etc.), Numerical methods for matrix equations, Matrix equations and identities, split quaternion matrix, Direct numerical methods for linear systems and matrix inversion

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