g-循环矩阵的谱分解和Jordan块结构  

Spectral Decomposition and Jordan Block Structure for g-Circulant Matrices

作　　者：张荣娥[1] 

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2002年第3期10-12,共3页Journal of Ningbo University：Natural Science and Engineering Edition

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 。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.

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 

分 类 号：O151.21[理学—数学]