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.
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.
