| 广义酉矩阵与广义Hermite矩阵 |
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| 引用本文： | 袁晖坪.广义酉矩阵与广义Hermite矩阵[J].数学杂志,2003,23(3):375-380. |
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| 作者姓名： | 袁晖坪 |
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| 作者单位： | 重庆工商大学数学系,重庆,400033 |
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| 基金项目： | 重庆市教委科学基金(980102) |
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| 摘 要： | 给出了广义酉矩阵与广义(斜)Hermite矩阵的概念，研究了它们的性质及其与酉阵、共轭辛阵、Hermite阵、Hamilton及广义逆矩阵之间的联系；取得了许多新的结果；推广了酉矩阵、Hermite阵与斜Hermite阵间的相应结果，特别将正交阵的广义Cayley分解推广到了广义酉矩阵上；将各类酉矩阵、Hermite矩阵及广义逆矩阵统一了起来．
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| 关 键 词： | 广义酉矩阵 广义Hermite阵 广义斜Hermite阵 广义逆矩阵 |
| 文章编号： | 0255-7797(2003)03-0375-06 |
GENERAILZED UNITARY MATRICES AND GENERALIZED HERMITE MATRICES |
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| YUAN Hui-ping.GENERAILZED UNITARY MATRICES AND GENERALIZED HERMITE MATRICES[J].Journal of Mathematics,2003,23(3):375-380. |
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| Authors: | YUAN Hui-ping |
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| Abstract: | The concepts of generalized unitary matrix and generalized (obilque)Hermite matrix are given, their properties and relations between they and unitary matrix, conjugate matrix,Hermite matris,Hamilton matrix and gereralized inverse matris are studied, and many new results are obtained. Moreover, the corresponding results on relations among unitary matrix,Hermite matrix and anit -Hermite matrix are popularized .especially the Cayley decomposition of orthogonal matrix is extended to generalized unitary matrix, and various kinds of the unitary matrix, Hermite matrix; generalized Hermite matrix and generalized inverse matrix unified. |
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| Keywords: | generalized unitary matrix generalized Hermite matrix generalized obilque Hermite matris generaliaed inverse matrix |
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