| 关于矩阵表示秩的研究及应用 |
| |
| 引用本文： | 江静,包玉宝,王婷.关于矩阵表示秩的研究及应用[J].山东师范大学学报(自然科学版),2013(3):9-11,15. |
| |
| 作者姓名： | 江静 包玉宝 王婷 |
| |
| 作者单位： | [1]齐鲁师范学院数学与应用数学系,济南250013 [2]山东师范大学数学科学学院,济南250014 |
| |
| 基金项目： | 山东省高等学校科技计划项目（J09LA55）;齐鲁师范学院青年基金资助项目（2012L1001）. |
| |
| 摘 要： | 考虑四元数体上的两个矩阵表达式A—BXB＊-CY—Y＊C＊和A—BXB＊-CY＋Y＊C＊，其中A是四元数上的埃尔米特矩阵或是斜埃尔米特矩阵．在四元数体上研究了这两个线性矩阵表达式的最大秩和最小秩，并且给出了满足最小秩时X和Y的一般形式．作为应用，通过矩阵秩的方法得到了一四元数矩阵方程相容的充要条件．
|
| 关 键 词： | 矩阵表达式 埃尔米特矩阵 最小秩 最大秩 |
RESEARCH ON THE RANK OF MATRIX EXPRESSIONS WITH APPLICATIONS |
| |
| Jiang Jing Bao Yubao Wang Ting.RESEARCH ON THE RANK OF MATRIX EXPRESSIONS WITH APPLICATIONS[J].Journal of Shandong Normal University(Natural Science),2013(3):9-11,15. |
| |
| Authors: | Jiang Jing Bao Yubao Wang Ting |
| |
| Institution: | Jiang Jing Bao Yubao Wang Ting ( 1 ) Department of Mathematics, Qilu Normal University,250013, Jinan, China; 2) School of Mathematics Science, Shandong Normal University, 250014, Jinan, China ) |
| |
| Abstract: | Considering A - BXB ＊ - CY - Y ＊ C ＊ and A - BXB ＊ - CY ＋ Y＊ C ＊ as two linear matrix expressions over quaternion algebra, where A is an Hermitian or skew - Hermitian matrix, we establish the formula of the maximal and minimal ranks of quaternion matrix expressions mentioned above. Moreover, we consider how to choose X and Y such that the two expressions attain the minimal possible ranks. As an application, we get the necessary and sufficient conditions for the consistence of quaternion matrix equation. |
| |
| Keywords: | matrix expressions Hermitian matrix minimal rank maximal rank |
| 本文献已被 维普 等数据库收录！ |
