@article{Jaiprasert2024, 
author = {Janthip Jaiprasert and Pattrawut Chansagiam},
title = {Exact and least-squares solutions of a generalized Sylvester-transpose matrix equation over generalized quaternions},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {4},
pages = {2789-2804},
keywords = {generalized Sylvester-transpose matrix equation, generalized quaternion matrix, minimal norm solution, least-squares solution, vector operator, Kronecker product},
url = {https://www.sciopen.com/article/10.3934/era.2024126},
doi = {10.3934/era.2024126},
abstract = {We have considered a generalized Sylvester-transpose matrix equation    A  X  B  +  C      X    T    D  =  E  , where    A  ,  B  ,  C  ,  D  , and    E are given rectangular matrices over a generalized quaternion skew-field, and    X is an unknown matrix. We have applied certain vectorizations and real representations to transform the matrix equation into a matrix equation over the real numbers. Thus, we have investigated a solvability condition, general exact/least-squares solutions, minimal-norm solutions, and the exact/least-squares solution closest to a given matrix. The main equation included the equation    A  X  B  =  E and the Sylvester-transpose equation. Our results also covered such matrix equations over the quaternions, and quaternionic linear systems.}
}