The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation AXA∗=B

A General Hermitian Nonnegative-Definite Solution to the Matrix Equation <i>AXB</i> = <i>C</i>

“…solution and a new representation of the general Hermitian n.n.d. solution to (1). Moreover, our representation is invariant with respect to the generalized inverse (g-inverse) involved, unlike the solution from Khatri in [6].…”

“…Hermitian solutions to (1) have been considered by numerous authors as well such as by Khatri in [6], Wang, Yan, and Dai in [7], and Cvetković-Ilić in [8].…”

“…solution and a representation of a general Re-n.n.d. solution to (1). Also, Zhang has proposed representations of the general Hermitian n.n.d.…”

“…Moreover, our representation is invariant with respect to the generalized inverse (g-inverse) involved, unlike the solution from Khatri in [6]. We then apply our solution to an example problem posed by Zhang in [1] and obtain a simpler solution that contradicts the proposed solution from Zhang in [1]. Furthermore, while Zhang employs an algorithmic method in [1], we obtain a closed-form solution.…”

The reflexive re-nonnegative definite solution to a quaternion matrix equation

“…For instance, Khatri and Mitra [3], Baksalary [4], Groβ [5], Zhang and Cheng [6] derived the general Hermitian positive semidefinite solution to matrix equation (1.1), respectively. Moreover, Dai and Lancaster [7] studied the similar problem and emphasized the importance of (1.1) within the real setting.…”