四元数Hermitian张量的特征值反问题及最佳逼近  

The Inverse Eigenvalue Problem of Quaternion Hermitian Tensors and Its Best Approximation

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,广西南宁530006

出　　处：《昆明理工大学学报（自然科学版）》2022年第6期182-188,共7页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(11661011).

摘　　要：提出并讨论Einstein积下四元数Hermitian张量的特征值反问题,即给定s个四元数张量特征对,寻找四元数Hermitian张量B使其包含这些特征对.通过把原问题转化为一个无约束张量方程的方法,并利用张量Moore-Penrose广义逆,得到了关于张量B的可解条件及其通解表达式.同时,对于给定四元数张量,得到了Frobenius范数意义下上述反问题解集中的唯一最佳逼近解.最后应用数值例子检验了所给方法的可行性.The inverse eigenvalue problem of quaternion Hermitian tensors under Einstein product is proposed and discussed, that is, given s quaternion tensor feature pairs, look for the quaternion Hermitian tensor B to include these feature pairs.By transforming the original problem into an unconstrained tensor equation and using the tensor Moore-Penrose generalized inverse, the solvable conditions and general solution expression of the tensor B are obtained.At the same time, for a given quaternion tensor, the unique best approximation solution of the solution set of the above inverse problem in the sense of Frobenius norm is obtained.Finally, a numerical example is used to test the feasibility of the given method.

关 键 词：四元数 Hermitian张量 特征值反问题 Einstein积 最佳逼近 

分 类 号：O151.21[理学—数学]