华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (2): 56-62,68.doi: 10.3969/j.issn.1000-5641.2019.02.006

• 数学 • 上一篇    下一篇

一类Hamilton矩阵逆的填充

白晓丽, 张澜   

  1. 内蒙古工业大学 理学院, 呼和浩特 010051
  • 收稿日期:2018-03-26 出版日期:2019-03-25 发布日期:2019-03-27
  • 通讯作者: 张澜,女,副教授,研究方向为算子谱理论.E-mail:zhanglanfw@163.com E-mail:zhanglanfw@163.com
  • 作者简介:白晓丽,女,硕士研究生,研究方向为算子谱理论.E-mail:544870462@qq.com.
  • 基金资助:
    国家自然科学基金（71561020）；内蒙古自治区自然科学基金（2018MS01002）

Inverse completion for a class of Hamiltonian matrices

BAI Xiao-li, ZHANG Lan   

  1. College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China
  • Received:2018-03-26 Online:2019-03-25 Published:2019-03-27

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摘要： 本文利用矩阵秩理论和矩阵可逆的条件，研究了一类Hamilton矩阵逆的填充问题.充分利用Hamilton矩阵的结构特点，证明其有解的充分必要条件，并得到解的表示.进一步将结论推广到反Hamilton矩阵上，得到相应的结果.最后用实例对结论加以验证.

关键词: 矩阵填充, 块矩阵, Hamilton矩阵, 反Hamilton矩阵

Abstract: In this paper, the inverse completion of a class of Hamiltonian matrices is studied by applying rank theory and invertible conditions for matrices. Taking advantage of the structural characteristics of Hamiltonian matrices, the sufficient and necessary conditions for the existence of solutions are proved and the expression of solutions are obtained. Furthermore, the conclusions are extended to anti-Hamiltonian matrices, and the corresponding results are obtained. Finally, some examples are used to verify the conclusions.

Key words: matrix completion, block matrix, Hamiltonian matrix, antiHamiltonian matrix

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