华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (2): 5-11.doi: 10.3969/j.issn.1000-5641.2023.02.002

• 数学 • 上一篇    下一篇

Hermite R-反对称矩阵的二次特征值反问题

齐志萍(), 张澜*()   

  1. 内蒙古工业大学 理学院, 呼和浩特　010051
  • 收稿日期:2021-04-02 出版日期:2023-03-25 发布日期:2023-03-23
  • 通讯作者: 张澜 E-mail:1546617949@qq.com;zhanglanfw@163.com
  • 基金资助:
    内蒙古自治区自然科学基金(2018MS01002)

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

Zhiping QI(), Lan ZHANG*()   

  1. College of Sciences, Inner Mongolia University of Technology, Hohhot　010051, China
  • Received:2021-04-02 Online:2023-03-25 Published:2023-03-23
  • Contact: Lan ZHANG E-mail:1546617949@qq.com;zhanglanfw@163.com

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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

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

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