一类四元数共轭辛张量的特征值反问题  

The Inverse Eigenvalue Problem for a Class of Quaternion Conjugate Symplectic Tensors

作　　者：白瑞 黄敬频[1] Bai Rui;Huang Jingpin(School of Mathematics and Physics,Guangxi University for Nationalities,Nanning 530006,China)

机构地区：[1]广西民族大学数学与物理学院,南宁530006

出　　处：《数学理论与应用》2023年第2期92-106,共15页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.11661011)资助。

摘　　要：本文研究在Einstein积下一类四元数共轭辛张量的特征值反问题.首先,利用四元数张量的转换算子得到共轭辛张量的性质及特征结构.其次,对给定的I_(1)I_(2)…I_(N)个四元数张量特征对,找到四元数自共轭辛张量S使其包含所给的全部特征对.作为应用,我们给出四元数张量方程S_(*N)S=D存在共轭辛张量解的充要条件及解的表达式,并用数值算例检验所给方法的可行性.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)…I_(N) characteristic pairs of quaternion tensors,a quaternion selfconjugated symplectic tensor 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 B_(∗N) S=D.The feasibility of the proposed method is showed with numerical examples.

关 键 词：四元数 Einstein积 共轭辛张量 特征结构 特征值反问题 

分 类 号：O241.6[理学—计算数学]