哈密尔顿-凯莱定理在多项式矩阵上的推广

摘要

哈密尔顿-凯莱定理是高等代数中一个经典的结论 ,它揭示了方阵和它对应的特征多项式之间的关系 .本文将此定理推广至多项式矩阵上 ,给出了多项式矩阵及其行列式之间的一种关系 ,使经典的哈密尔顿-凯莱定理成为本文中定理的一种特殊情况 .%Cayley-Hamilton Theorem is a classical conclusion in advanced algebra .It reveals the relationship between the square matrix and its corresponding characteristic polynomial .This paper will generalize the classical Cayley-Hamilton Theorem for polynomial matrix .One relationship between the polynomial matrix and its determinant will be given .So it makes the classical Cayley-Hamilton Theorem a special case of the theorem in this paper .