| 引用本文: | 冯良贵,罗继红.基于四元数体上的几个矩阵不等式.[J].国防科技大学学报,2009,31(3):136-140.[点击复制] |
| FENG Lianggui,LUO Jihong.Several Matrix Inequalities in Quaternion Algebra[J].Journal of National University of Defense Technology,2009,31(3):136-140[点击复制] |
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| 基于四元数体上的几个矩阵不等式 |
| 冯良贵, 罗继红 |
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(国防科技大学 理学院，湖南 长沙 410073)
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| 摘要: |
| 四元数矩阵的特征值与奇异值在四元数矩阵理论的应用中起着重要作用。借助于分块矩阵及相关恒等式，给出了关于四元数矩阵特征值与奇异值的几个新的不等式，推广了实或复数域上矩阵特征值与奇异值不等式的相应结果，它们可望有助于推动四元数代数在量子力学、机器人技术等学科中的进一步应用。 |
| 关键词: 自共轭 正定 特征值 奇异值 |
| DOI： |
| 投稿日期：2008-09-12 |
| 基金项目:新世纪优秀人才计划项目(NCET)；国防科技大学基础研究资助项目(JC08-02-03) |
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| Several Matrix Inequalities in Quaternion Algebra |
| FENG Lianggui, LUO Jihong |
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(College of Science, National Univ. of Defense Technology, Changsha 410073, China)
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| Abstract: |
| The eigenvalue and the singular value of a quatemion matrix play important roles in the applications of quaternion matrix theory. By virtue of the blocked matrix and the corresponding identities, several inequalities on the eigenvalue and the singular value of quaternion matrices are established, which generalize the corresponding results existing in the real or the complex matrix theory. The results of this paper may help to improve the applications of quaternion algebra in such related fields as quantum mechanics, robot technology and the like. |
| Keywords: self-conjugation positive definite singular value eigenvalue |
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