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J4 ›› 2010, Vol. 45 ›› Issue (4): 106-110.

• 论文 • 上一篇    

分块Hermite阵与斜Hermite阵的最大秩与最小秩

张凤霞1,李莹1,2,郭文彬1,赵建立1   

  1. 1. 聊城大学数学科学学院, 山东 聊城 252059; 2. 上海理工大学管理学院, 上海 200093
  • 收稿日期:2009-09-09 出版日期:2010-04-10 发布日期:2010-05-19
  • 作者简介:张凤霞(1977-),女,讲师,硕士,从事矩阵论研究.Email: zhangfengxia@lcu.edu.cn
  • 基金资助:

    国家自然科学基金资助项目(10771073)

Extremal ranks for block Hermitian and skew-Hermitian matrices

ZHANG Feng-xia1, LI Ying1,2, GUO Wen-bin1,  ZHAO Jian-li1   

  1. 1. College of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China;
    2. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2009-09-09 Online:2010-04-10 Published:2010-05-19

摘要:

利用有关Hermite阵、斜Hermite阵的几个表达式的秩与分块矩阵的性质,研究了分块Hermite阵{AB*BX}在无其他约束条件和满足约束条件BXB*=A(A=A*)下的最大秩与最小秩,与分块斜Hermite阵{A-B*BX}在无约束条件和满足约束条件BXB*=A(A=-A*)下的最大秩与最小秩。

关键词: 分块Hermite阵;分块斜Hermite阵;最大秩;最小秩

Abstract:

In this paper, by using the ranks of several expressions about Hermitian matrices and skew-Hermitian matrices and the characters of block matrices, the maximal ranks and minimal ranks of the block Hermitian {AB*BX} with respect to X are investigated, where X is an arbitrary Hermitian matrices or X is the Hermitian solutions to the matrix equation BXB*=A(A=A*). And the maximal ranks and minimal ranks of the block skewHermitian matrix {A-B*BX}with respect to X are investigated, where X is an arbitrary skew-Hermitian matrix or X is the skew-Hermitian solutions to the matrix equation BXB*=A(A=-A*).

Key words: block Hermite matrices; block skew-Hermite matrices; maximal rank; minimal rank

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