| Issue |
4open
Volume 2, 2019
Advances in Researches of Quaternion Algebras
|
|
|---|---|---|
| Article Number | 24 | |
| Number of page(s) | 15 | |
| Section | Mathematics - Applied Mathematics | |
| DOI | https://doi.org/10.1051/fopen/2019021 | |
| Published online | 09 July 2019 | |
Review Article
Cramer’s rules for the system of quaternion matrix equations with η-Hermicity
Pidstrygach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Lviv 79060, Ukraine
* Corresponding author: st260664@gmail.com
Received:
10
January
2019
Accepted:
6
June
2019
The system of two-sided quaternion matrix equations with η-Hermicity, A1XA1η* = C1, A2XA2η* = C2 is considered in the paper. Using noncommutative row-column determinants previously introduced by the author, determinantal representations (analogs of Cramer’s rule) of a general solution to the system are obtained. As special cases, Cramer’s rules for an η-Hermitian solution when C1 = Cη*1 and C2 = Cη*2 and for an η-skew-Hermitian solution when C1 = −Cη*1 and C2 = −Cη*2 are also explored.
Mathematics Subject Classification: 15A24 / 15A15 / 15A09 / 15B33
Key words: Generalized inverse / Noncommutative determinant / Quaternion matrix / System of matrix equations / Cramer rule / η-Hermicity
© I.I. Kyrchei, Published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.