| 具有奇异值分解性质的代数 |
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| 引用本文： | 黄礼平.具有奇异值分解性质的代数[J].数学学报,1997,40(2):161-166. |
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| 作者姓名： | 黄礼平 |
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| 作者单位： | 湘潭矿业学院基础科学部 湘潭411201 |
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| 基金项目： | 中国科学院数学研究所访问学者基金 |
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| 摘 要： | 设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域.
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| 关 键 词： | 域上代数 奇异值分解 广义四元数代数 Galois序闭域 酉矩阵 |
| 收稿时间： | 1995-10-16 |
The Algebras Having Singular Value Decomposition Property |
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| Huang Liping.The Algebras Having Singular Value Decomposition Property[J].Acta Mathematica Sinica,1997,40(2):161-166. |
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| Authors: | Huang Liping |
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| Institution: | Huang Liping (Department of Basic Sciences, Xiangtan Mining Institute, Xiangtan 411201, China) |
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| Abstract: | Let F be a field, R an F-algebra with an involution, if any matrix over R has a singular value decomposition (SVD for short), then R is said to have the SVD property. This paper shows that: R is an F-algebra having the SVD property if and only if R is isomorphic to either R or R (-1~1/-1) or the quaternion field (-1,-1/R ) over R , where R is the set of all symmetric elements of R, and R is a Galois order closed field. |
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| Keywords: | Algebra over a field Singular value decomposition Generalized quaternion algebra Galois order closed field Unitary matrix |
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