| 半正定自共轭四元数矩阵广义逆的单调性问题 |
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| 引用本文： | 庄瓦金.半正定自共轭四元数矩阵广义逆的单调性问题[J].数学学报,1996,39(2):268-274. |
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| 作者姓名： | 庄瓦金 |
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| 作者单位： | 漳州师范学院教学系 |
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| 摘 要： | 对于四元数矩阵的Ｌｏｗｎｅｒ偏序，设０≤Ｂ≤Ａ．本文利用（ｎ，≥）中矩阵的同时合同化简，给出了Ｂ｛１；≥；ｓ；≥Ａ（１）｝的表式，以及下面三个单调性结论的特征刻划：ｉ）Ｂ（１）∈Ｂ｛１；＊｝，Ａ｛１；＊；≤Ｂ（１）｝≠；０；ｉｉ）０≤Ｂ（１，２）≤Ｂ（１，２）≤Ａ（１，２）；ｉｉｉ）Ａ（１，２）∈Ａ｛１，２；≥｝，Ｂ｛１，２；≥；≤Ａ（１，２）｝只含一个元素．
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| 关 键 词： | 半正定自共轭四元数矩阵，Lowner偏序，广义逆，同时合同化简 |
| 收稿时间： | 1994-4-20 |
| 修稿时间： | 1995-2-2 |
The Monotonicity Problems for Generalized Inverses or Positive Semidefinite Self-Conjugate Quaternion Matrices |
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| Zhuang Wajin.The Monotonicity Problems for Generalized Inverses or Positive Semidefinite Self-Conjugate Quaternion Matrices[J].Acta Mathematica Sinica,1996,39(2):268-274. |
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| Authors: | Zhuang Wajin |
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| Institution: | Zhuang Wajin(Department of Mathematics, Zhangzhou Normal College, Zhangzhou 363000, China) |
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| Abstract: | Let 0 ≤B≤ A for the Lowner's partial ordering of quateraion matrices. In this paper, we give a representation formula of the solution set B{1;≥ ;≥ a; A(1)} of a monotonicity.Some characterizations of three monotonicity conclusions of the generalized inverses of A and Bare obtained. |
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| Keywords: | positive semidefinite self-conjugate quaternion matrix Lowner's partial ordering generalized inverse simultaneous reduction by congruence |
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