哈密尔顿-凯莱定理的应用

The Application of Hamilton-cayley Theorem

在处理矩阵问题时,利用特征理论是一大方法.哈密尔顿-凯莱定理揭示了方阵和它对应的特征多项式之间的关系,是特征多项式所具有的一个重要性质.除在理论上极为重要外,对解决某些具体问题也有独特的用处.结合实例,介绍了哈密尔顿-凯莱定理在证明及求方阵的逆阵、方阵的高阶幂中的应用.

Taking advantage of feature theory is an important way in dealing with the matrix problem. Hamilton-cayley Theorem reveals the relationship between the matric and its feature polgnomial . It is not only very important in theory,but also convenient in dealing with some concrete problems. Application of Hamilton-cayley Theorem in improving some conclusion and the computation of inverse matrix and matrix power is discussed by exampl ification.