Filomat 2022 Volume 36, Issue 3, Pages: 887-903
https://doi.org/10.2298/FIL2203887Y
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The common solution of twelve matrix equations over the quaternions
Yuan Wei-Jie (Department of Mathematics, Shanghai University, Shanghai, P.R. China), weijievicky@163.com
Wang Qing-Wen (Department of Mathematics, Shanghai University, Shanghai, P.R. China + Collaborative Innovation Center for the Marine Artificial Intelligence, Shanghai, China), wqw@t.shu.edu.cn
In this paper, we investigate a system of twelve quaternion matrix equations.
Using the real representation of a quaternion matrix, we first derive the
least-squares solution with the least norm to the system. Meanwhile, we
establish the solvability conditions and an expression of the general
solution to the system when it is consistent.
Keywords: General solution, Least-squares solution, Least norm, Quaternion algebra, Real representation, Matrix equation
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