| 分块Hermite阵与斜Hermite阵的最大秩与最小秩 |
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| 引用本文： | 张凤霞,李莹,郭文彬,赵建立.分块Hermite阵与斜Hermite阵的最大秩与最小秩[J].山东大学学报(理学版),2010,45(4):106-110. |
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| 作者姓名： | 张凤霞 李莹 郭文彬 赵建立 |
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| 作者单位： | 1. 聊城大学数学科学学院,山东,聊城,252059
2. 聊城大学数学科学学院,山东,聊城,252059;上海理工大学管理学院,上海,200093 |
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| 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ABB*X]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ABB*X]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。
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| 关 键 词： | 分块Hermite阵 分块斜Hermite阵 最大秩 最小秩 |
| 收稿时间： | 2009-09-09 |
Extremal ranks for block Hermitian and skew-Hermitian matrices |
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| ZHANG Feng-xia,LI Ying,GUO Wen-bin,ZHAO Jian-li.Extremal ranks for block Hermitian and skew-Hermitian matrices[J].Journal of Shandong University,2010,45(4):106-110. |
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| Authors: | ZHANG Feng-xia LI Ying GUO Wen-bin ZHAO Jian-li |
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| Institution: | 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 |
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| 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 matrix(A B B* X) with respect to X are investigated, where X is an arbitrary Hermitian matrices or X is the Hermitian solutions to the matrix equation XB*=A(A=A*). And the maximal ranks and minimal ranks of the block skew-Hermitian matrix (A B -B* X)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*). |
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| Keywords: | block Hermite matrices block skew-Hermite matrices maximal rank minimal rank |
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