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ABSTRACT
In this paper, we establish some conditions for the existence and the representations for the Hermitian reflexive and Hermitian anti-reflexive, and non-negative definite reflexive solutions to the matrix equation AX=B with respect to a generalized reflection matrix P by using the Moore–Penrose inverse. Moreover, in corresponding solution sets of the equation, the explicit expressions of the nearest matrix to a given matrix in the Frobenius norm have been provided.
Acknowledgements
The author would like to thank the Editor and the referees for their very detailed comments and valuable suggestions which greatly improved the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Funding
This work was supported by the National Natural Science Foundation of China [Grant Nos. 11661036, 11461026], and the Doctoral Scientific Research Foundation of Chongqing Normal University [Grant No. 17XLB004].