MR2333598 Jia, Zhi-gang; Zhao, Jian-li; Li, Ying; Jiang, Tong-song
One kind of inverse eigenvalue problems and its applications in
quaternionic quantum mechanics. Gongcheng Shuxue Xuebao 24 (2007),
no. 2, 343--347. 65F18 (81Q99)

In a fairly vaguely specified global context of physics a
motivation is found for two problems in the manipulation with
matrices over quaternions. The first one is an inversion of the
usual problem of determination of eigenvalues (now, eigenvectors
and eigenvalues are given), the second one is its certain least
square extension. The necessary and sufficient conditions of the
existence of the solutions are found, and the explicit formulae
and a numerical illustration are provided.