Ela the Reflexive Re-nonnegative Definite Solution to a Quaternion Matrix Equation∗

Abstract

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∗ = B, where ∗ 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 A1X1A1 + A2X2A ∗ 2 = B. The representation of such solution to the matrix equation is given.

Cite this paper

@inproceedings{Wang2008ElaTR, title={Ela the Reflexive Re-nonnegative Definite Solution to a Quaternion Matrix Equation∗}, author={Qing-Wen Wang}, year={2008} }