## Abstract and Applied Analysis

### Determinantal Representations of General and (Skew-)Hermitian Solutions to the Generalized Sylvester-Type Quaternion Matrix Equation

Ivan I. Kyrchei

#### Abstract

In this paper, we derive explicit determinantal representation formulas of general, Hermitian, and skew-Hermitian solutions to the generalized Sylvester matrix equation involving $⁎$-Hermicity $\mathbf{A}\mathbf{X}{\mathbf{A}}^{⁎}+\mathbf{B}\mathbf{Y}{\mathbf{B}}^{⁎}=\mathbf{C}$ over the quaternion skew field within the framework of the theory of noncommutative column-row determinants.

#### Article information

Source
Abstr. Appl. Anal., Volume 2019 (2019), Article ID 5926832, 14 pages.

Dates
Accepted: 18 December 2018
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.aaa/1551150389

Digital Object Identifier
doi:10.1155/2019/5926832

Mathematical Reviews number (MathSciNet)
MR3901847

Zentralblatt MATH identifier
07054490

#### Citation

Kyrchei, Ivan I. Determinantal Representations of General and (Skew-)Hermitian Solutions to the Generalized Sylvester-Type Quaternion Matrix Equation. Abstr. Appl. Anal. 2019 (2019), Article ID 5926832, 14 pages. doi:10.1155/2019/5926832. https://projecteuclid.org/euclid.aaa/1551150389

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