Special arrowhead least squares solution of the quaternion generalized Sylvester matrix equation

In this paper, we study special arrowhead solution of the quaternion generalized Sylvester matrix equation by using semi-tensor product of matrices. We first propose a real vector representation of quaternion matrix and study its properties. By means of this real vector representation, semi-tensor p...

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Bibliographic Details
Main Authors: Ding, Wenxv, Li, Ying, Wang, Dong, Wei, Anli
Format: Conference Proceeding
Language:English
Subjects:
Arithmetic
arrowhead matrices
Computational efficiency
Data mining
least squares solution
Mathematical models
Quaternion matrix equation
Quaternions
real column(row) stacking form
Redundancy
semi-tensor product of matrices
Stacking
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Summary:In this paper, we study special arrowhead solution of the quaternion generalized Sylvester matrix equation by using semi-tensor product of matrices. We first propose a real vector representation of quaternion matrix and study its properties. By means of this real vector representation, semi-tensor product of matrices and Moore-Penrose inverse, we solve the least squares arrowhead Hermitian (skew-Hermitian) problem of the quaternion generalized Sylvester matrix equation. The expressions of these solutions only involve real arithmetic, which makes the procedure computation more flexible and efficient.
ISSN:2161-2927
DOI:10.23919/CCC52363.2021.9549577