The bi-self-conjugate and nonnegative definite solutions to the inverse eigenvalue problem of quaternion matrices (Q2569261)

The so called ``bi-self-conjugate and non-negative definite matrices'' in the framework of the inverse eigenvalue problem of quaternionic matrices [cf \textit{W. Zhuang}, Acta Math. Sci., Ser. A, Chin. Ed. 24, No.~5, 583--588 (2004; Zbl 1064.15021)] are introduced and studied. The general expressions for the bi-self-conjugate quaternionic matrices are obtained. The solvability condition for the inverse eigenvalue problem in set of quaternionic \(n\times n\) matrices is given. At last, the necessary and sufficient conditions for existence of all \(n\times n\)-quaternionic matrices which are bi-self-conjugate and nonnegative definite are established.