| g-循环矩阵的谱分解和Jordan块结构 |
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| 引用本文： | 张荣娥. g-循环矩阵的谱分解和Jordan块结构[J]. 宁波大学学报(理工版), 2002, 15(3): 10-12 |
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| 作者姓名： | 张荣娥 |
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| 作者单位： | 宁波大学,理学院,浙江,宁波,315211 |
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| 摘 要： | 首先证明了n级非奇异g-循环矩阵必定可以对角化，并且给出了它的谱分解。其次，当（n,g）=1时，给出了n级奇异g-循环矩阵相似于某些对角阵和某些幂零Jordan块的直和，进一步给出了其中幂零Jordan块的幂零指数的计算法。
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| 关 键 词： | 结构 g－循环矩阵 对角化 谱分解 幂零指数 幂零Jordan块 直和 |
| 文章编号： | 1001-5132(2002)03-0010-03 |
| 修稿时间： | 2001-10-31 |
Spectral Decomposition and Jordan Block Structure for g-Circu lant Matrices |
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| ZHANG Rong-e. Spectral Decomposition and Jordan Block Structure for g-Circu lant Matrices[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 2002, 15(3): 10-12 |
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| Authors: | ZHANG Rong-e |
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| Abstract: | The eigenstructure of g-circulant matrices are studied. Firstly, the nonsingular g-circulant matrices are similar to diagnal matrices. The spectral decomposition is given. Secondly, the singular g-circulant matrices are similar to the direct sum of some diagnal matrices and some nilpotency of Jordan blocks when (n,g)=1. Further, the nilpotency index of Jordan block is defined. |
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| Keywords: | g-circulant matrix diagonal spectral decomposition nilpotency index |
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