Constrainted least squares solution of Sylvester equation

Wenxv Ding; Ying Li; Dong Wang; AnLi Wei; Wenxv Ding; Ying Li; Dong Wang; AnLi Wei

doi:10.3934/mmc.2021009

Mathematical Modelling and Control

2021, Volume 1, Issue 2: 112-120. doi: 10.3934/mmc.2021009

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Research article

Constrainted least squares solution of Sylvester equation

Research Center of Semi-tensor Product of Matrices: Theory and Applications, College of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, China

Received: 18 March 2021 Accepted: 20 June 2021 Published: 23 June 2021

In this paper, we study several constrainted least squares solutions of quaternion Sylvester matrix equation. We first propose a real vector representation of quaternion matrix and study its properties. By using this real vector representation, semi-tensor product of matrices, swap matrix and Moore-Penrose inverse, we derive compatible conditions and the expressions of several constrainted least squares solutions of quaternion Sylvester equation.
- quaternion matrix equation,
- least squares solution,
- semi-tensor product of matrices,
- real vector representation,
- (anti)$ \eta $-Hermitian matrix
Citation: Wenxv Ding, Ying Li, Dong Wang, AnLi Wei. Constrainted least squares solution of Sylvester equation[J]. Mathematical Modelling and Control, 2021, 1(2): 112-120. doi: 10.3934/mmc.2021009

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Abstract

In this paper, we study several constrainted least squares solutions of quaternion Sylvester matrix equation. We first propose a real vector representation of quaternion matrix and study its properties. By using this real vector representation, semi-tensor product of matrices, swap matrix and Moore-Penrose inverse, we derive compatible conditions and the expressions of several constrainted least squares solutions of quaternion Sylvester equation.

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