Geodesic
The reflexive re-nonnegative definite solution to a quaternion matrix equation
The electronic journal of linear algebra, Tome 17 (2008), pp. 88-101.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper a necessary and sufficient condition is established for the existence of the reflexive re-nonnegative definite solution to the quaternion matrix equation AXA $\ast = B$, where $\ast $stands for conjugate transpose. The expression of such solution to the matrix equation is also given. Furthermore, a necessary and sufficient condition is derived for the existence of the general re-nonnegative definite solution to the quaternion matrix equation A 1 X 1 A $\ast 1$ + A 2 X 2 A $\ast 2$ = B. The representation of such solution to the matrix equation is given.
Classification : 65F05, 15A24, 15A33, 15A57
Keywords: quaternion matrix equation, reflexive matrix, re-nonnegative definite matrix, reflexive re-nonnegative definite matrix 
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     title = {The reflexive re-nonnegative definite solution to a quaternion matrix equation},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/ELA_2008__17__a37/}
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Wang, Qing-Wen; Zhang, Fei. The reflexive re-nonnegative definite solution to a quaternion matrix equation. The electronic journal of linear algebra, Tome 17 (2008), pp. 88-101. http://geodesic.mathdoc.fr/item/ELA_2008__17__a37/