| 四元数自共轭矩阵特征值的变分特征及其应用 |
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| 引用本文： | 李莹,赵建立. 四元数自共轭矩阵特征值的变分特征及其应用[J]. 河北大学学报(自然科学版), 2009, 29(2): 116. DOI: 10.3969/j.issn.1000-1565.2009.02.002 |
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| 作者姓名： | 李莹 赵建立 |
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| 作者单位： | 上海理工大学,管理学院,上海,200093;聊城大学,数学科学学院,山东,聊城,252059;聊城大学,数学科学学院,山东,聊城,252059 |
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| 摘 要： | 利用四元数矩阵的复表示及友向量的概念结合复数域上的Hermitian阵的性质证明了四元数自共轭矩阵的特征值的变分特征,并利用变分特征研究了四元数矩阵特征值的性质.得到了四元数矩阵的Wey1定理、单调性定理、柯西分隔定理等一系列结果.
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| 关 键 词： | 四元数自共轭矩阵 特征值 变分特征 Hermitian阵 |
Variational Characterizations of Eigenvalues of Self-conjugate Quaternion Matrix and Its Application |
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| LI Ying,ZHAO Jian-li. Variational Characterizations of Eigenvalues of Self-conjugate Quaternion Matrix and Its Application[J]. Journal of Hebei University (Natural Science Edition), 2009, 29(2): 116. DOI: 10.3969/j.issn.1000-1565.2009.02.002 |
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| Authors: | LI Ying ZHAO Jian-li |
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| Affiliation: | 1.College of Management;University of Shanghai for Science and Technology;Shanghai 200093;China;2.College of Mathematics Science;Liaocheng University;Liaocheng 252059;China |
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| Abstract: | Variational characterizations of eigenvalues of self-conjugate quaternion matrices was proved by using of the concept of complex presentation of quaternion matrix and companion vector and the properties of Hermitian matrix.A series of results such as Weyl theorem,monotonicity theorem and Cauchy separating theorem was gotten by the variational characterizations. |
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| Keywords: | self-conjugate quaternion matrix eigenvalue variational characterization Hermitian matrix |
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