JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 103-110.doi: 10.6040/j.issn.1671-9352.0.2020.682

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Solutions of the quaternion matrix equation based on semi-tensor product of matrices

DING Wen-xu, LI Ying*, WANG Dong, ZHAO Jian-li   

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng 252000, Shandong, China
  • Published:2021-06-03

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Abstract: A new kind of real vector representation of quaternion matrix is proposed which is applied to study the Hermitian or anti-Hermitian solution of the quaternion matrix equation. Combined this real vector representation with semi-tensor product of matrics, the problem of quaternion matrix equation is transformed into the corresponding problem in real number field. And then, by studying the structural characteristics of quaternion Hermitian matrix and anti-Hermitian matrix, the useful information in the real vector representation is extracted and the redundancy is removed, then the original problem is simplified by reducing the dimension. This method can be applied to similar problems with different constraint.

Key words: quaternion matrix equation, semi-tensor product of matrices, swap matrix, real vector representation, Hermitian(anti-Hermitian)matrix

CLC Number: 

  • O241.6
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