关键词: 四元数, Einstein积, 共轭辛张量, 特征结构, 特征值反问题

Abstract:

This paper studies the inverse eigenvalue problem for a class of quaternion conjugate symplectic tensors under the Einstein product. Firstly, the properties and characteristic structures of conjugate symplectic tensors are obtained by using the transformation operator of quaternion tensors. Secondly, for the given ${I_1}{I_2} \cdots {I_N}$ characteristic pairs of quaternion tensors, a quaternion self-conjugated symplectic tensor $\mathcal{S}$ is found to include all the given characteristic pairs. As an application,

we give a necessary and sufficient condition for the existence of conjugate symplectic tensor solutions and the expression of solutions to the quaternion tensor equation $\mathcal{B}\ast_{N}\mathcal{S} = \mathcal{D}$. The feasibility of the proposed method is showed with numerical examples.

Key words: Quaternion, Einstein product, Conjugate symplectic tensor, Characteristic structure, Inverse eigenvalue problem