| 对Cayle-Hamilton定理的证明及推广研究 |
| |
| 引用本文： | 栗裕,郭红梅.对Cayle-Hamilton定理的证明及推广研究[J].长春师范学院学报,2011(12):4-5. |
| |
| 作者姓名： | 栗裕 郭红梅 |
| |
| 作者单位： | 山西体育职业学院;山西生物应用职业技术学院 |
| |
| 摘 要： | 矩阵理论中的Cayle-Hamilton定理,具有重要的理论价值和实用价值.本文利用矩阵的标准形和有关矩阵的乘法运算法则,对Cayle-Hamilton定理提出一种新的简明证法;并在定理证明的基础上,将此定理进行推广,证明以方阵A为根的矩阵多项式的行列式也A以为根.此推论的应用更具广泛性和一般性.
|
| 关 键 词： | Cayle-Hamilton定理 矩阵 Jordan标准形 |
A Research on the Proof and Generalization of Cayley-Hamilton Theorem |
| |
| LI Yu,GUO Hong-mei.A Research on the Proof and Generalization of Cayley-Hamilton Theorem[J].Journal of Changchun Teachers College,2011(12):4-5. |
| |
| Authors: | LI Yu GUO Hong-mei |
| |
| Institution: | 1.Shanxi Vocational College of Sports,Taiyuan 030006,China;2.Shanxi Professional Technology Institute of Biological Application,Taiyuan 030031,China) |
| |
| Abstract: | The Cayley-Hamilton theorem in matrix theory has important theoretical and practical value.In this paper,a new concise proof method for the Cayley-Hamilton theorem is put forward using Jordan canonical form and some multiplication operation rules of matrix.Based on the theorem proof,the theorem is generalized to prove that the matrix polynomial and its determinant both take square matrix A as the root.The application of this inference possesses more extensiveness and generalization. |
| |
| Keywords: | Cayley-Hamilton theorem matrix Jordan canonical form |
| 本文献已被 CNKI 等数据库收录！ |
