| 引用本文: | 俞森,程薇,冯良贵.一类广义延拓四元数矩阵的奇异值分解.[J].国防科技大学学报,2010,32(3):153-155.[点击复制] |
| YU Sen,CHENG Wei,FENG Lianggui.Singular Value Decomposition for Generalized Extended Quaternion Matrix[J].Journal of National University of Defense Technology,2010,32(3):153-155[点击复制] |
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| 一类广义延拓四元数矩阵的奇异值分解 |
| 俞森, 程薇, 冯良贵 |
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(国防科技大学 理学院，湖南 长沙 410073)
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| 摘要: |
| 从普通四元数矩阵的奇异值分解出发，给出了具有行或列对称结构的一类四元数矩阵(即广义四元数延拓矩阵)的奇异值、奇异向量与其母矩阵的奇异值、奇异向量之间的定量关系，推广了现有文献的结果。理论分析和数值实验的结果表明，就一大类广义四元数延拓矩阵而言，仅用母矩阵进行奇异值分解不但可以节省计算量和存储量，而且不影响任何数值精度。 |
| 关键词: 四元数矩阵 广义延拓四元数矩阵 母矩阵 奇异值分解 |
| DOI： |
| 投稿日期：2009-10-19 |
| 基金项目:新世纪优秀人才专项资助项目(NCET06-09-23)；国防科技大学资助项目(JC08-02-03) |
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| Singular Value Decomposition for Generalized Extended Quaternion Matrix |
| YU Sen, CHENG Wei, FENG Lianggui |
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(College of Science, National Univ. of Defense Technology，Changsha 410073, China)
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| Abstract: |
| Based on the general singular value decompositions of quaternion matrices, a relationship of the singular values and singular vectors was given between the generalized extended quaternion matrix of symmetric rows or columns and its original quaternion matrix, which extends the existing results. Theoretical predictions and numerical evidences show that, for a class of extended matrices, the singular value decomposition using the original quaternion matrix rather than the generalized extended quaternion matrix can save dramatically the memory and alleviate considerably the computational burden without loss of any numerical precision. |
| Keywords: quaternion matrix generalized extended quaternion matrix original quaternion matrix singular value decomposition |
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