Abstract
In this paper, we establish the solvability conditions and the formula of the general solution to a Sylvester-like quaternion matrix equation. As an application, we give some necessary and sufficient conditions for a system of quaternion matrix equations to be consistent, and present an expression of the general solution of the system when it is solvable. We present an algorithm and an example to illustrate the main results of this paper. The findings of this paper generalize the known results in the literature.
Highlights
We mainly investigate the following matrix equation: Chen, J.-F.; Xie, Y.-Z
As an application of (1), we investigate the system of the following matrix equations: E1 X1 = F1, X1 G1 = H1, E1 X2 = F2, X2 G2 = H2, E2 X3 = F3, X3 G2 = H3, (4)
Throughout this paper, we denote the set of all real numbers by R, the set of all m × n quaternion matrices by Hm×n, where we obtain the following: H = {u0 + u1 i + u2 j + u3 k|i2 = j2 = k2 = ijk = −1, u0, u1, u2, u3 ∈ R}
Summary
We mainly investigate the following matrix equation: Chen, J.-F.; Xie, Y.-Z. Xie and Wang [20] derived a necessary and sufficient condition for (2) to have a reducible solution. They provided some necessary and sufficient conditions for (3). Equation (1) to have a solution, and derive an expression of the general solution to (1) when it is solvable. As an application of (1), we derive some necessary and sufficient conditions for the system of matrix Equations (4) to have a solution as well as an expression of its general solution. We give a brief conclusion to close this paper in In Section 4
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
