华东师范大学学报（自然科学版） >

2023 , Vol. 2023 >Issue 2: 5 - 11

DOI: https://doi.org/10.3969/j.issn.1000-5641.2023.02.002

数学

Hermite R-反对称矩阵的二次特征值反问题

  • 齐志萍 ,
  • 张澜
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  • 内蒙古工业大学 理学院, 呼和浩特　010051

收稿日期: 2021-04-02

  网络出版日期: 2023-03-23

基金资助

内蒙古自治区自然科学基金(2018MS01002)

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The Hermitian R-antisymmetric solution of an inverse quadratic eigenvalue problem

  • Zhiping QI ,
  • Lan ZHANG
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  • College of Sciences, Inner Mongolia University of Technology, Hohhot　010051, China

Received date: 2021-04-02

  Online published: 2023-03-23

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摘要

研究了Hermite R-反对称矩阵的二次特征值反问题. 利用矩阵分块法、奇异值分解、向量拉直和Moore-Penrose逆, 证明了该问题Hermite R-反对称解的存在性, 给出了Hermite R-反对称解的一般表达式, 讨论了最佳逼近问题. 并给出了算例验证理论的正确性.

关键词： Hermite R-反对称矩阵; 奇异值分解; 向量拉直; 最佳逼近

本文引用格式

齐志萍 , 张澜 . Hermite R-反对称矩阵的二次特征值反问题[J]. 华东师范大学学报（自然科学版）, 2023 , 2023(2) : 5 -11 . DOI: 10.3969/j.issn.1000-5641.2023.02.002

Abstract

In this paper, we consider the inverse problem of quadratic eigenvalue for a Hermitian R-antisymmetric matrix. By using the matrix block method, singular value decomposition, vector straightening, and the Moore-Penrose inverse, we prove the existence of a Hermitian R-antisymmetric solution. In addition, we provide the general expression for a Hermitian R-antisymmetric solution, and discuss the best approximation thereof. Finally, an example is offered to validate the theory.

Key words： Hermitian R-antisymmetric matrix; singular value decomposition; vector straightening; optimal approximation

参考文献

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