A real representation method for solving Yakubovich-\(j\)-conjugate quaternion matrix equation
type: Item
instance of: scholarly article
title: A real representation method for solving Yakubovich-\(j\)-conjugate quaternion matrix equation
zbMATH Open document ID: 1469.65081
DOI: 10.1155/2014/285086
author: Caiqin Song
author: Jianli Zhao
author: Jun-e Feng
author: Xiaodong Wang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A new approach is presented for obtaining the solutions to Yakubovich-\(j\)-conjugate quaternion matrix equation \(X - A \hat{X} B = C Y\) based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrix \(A\). The closed form solution is established and the equivalent form of solution is given for this Yakubovich-\(j\)-conjugate quaternion matrix equation. Moreover, the existence of solution to complex conjugate matrix equation \(X - A \overline{X} B = C Y\) is also characterized and the solution is derived in an explicit form by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrix equation over complex field is a special case of Yakubovich-\(j\)-conjugate quaternion matrix equation \(X - A \hat{X} B = C Y\). Numerical example shows the effectiveness of the proposed results.
Mathematics Subject Classification ID: 65F45
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93B55
zbMATH DE Number: 7022091
Wikidata QID: Q59037669
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/285086
OpenAlex ID: W2008569882
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description: scientific article; zbMATH DE number 7022091