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

This paper provides two direct methods for solving the split quaternion matrix equation where X is an unknown split quaternion η ‐Hermitian matrix, and A ,  B ,  C ,  D ,  E ,  F are known split quaternion matrices with suitable size. Our tools are the Kronecker product, Moore–Penrose generalized in...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-10, Vol.46 (15), p.15952-15971
Main Authors: Li, Ming‐Zhao, Yuan, Shi‐Fang, Jiang, Hua
Format: Article
Language:English
Subjects:
Algorithms
Generalized inverse
Quaternions
Representations
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Summary:This paper provides two direct methods for solving the split quaternion matrix equation where X is an unknown split quaternion η ‐Hermitian matrix, and A ,  B ,  C ,  D ,  E ,  F are 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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7273