【摘要】 针对复数域上矩阵多项式空间基的求解问题.借助复数域K上n阶矩阵A的Jordon标准形JA,给出A的一种特殊分解式,讨论矩阵多项式空间K[JA]={f(JA)|f(x)∈K[x]}的基及其子空间的直和分解,进而确定复数域上矩阵多项式空间K[A]的一个关于子空间的直和分解式及其一组基.结果表明:利用子空间的直和分解式求解矩阵多项式空间的基方便可行.更多还原

【Abstract】 According to the problems of solving the base on subspaces of matrix polynomial space over the complex field,Let A is a square matrix of the complex field K and JA is the Jordon canonical form of A,a special decomposition of A is given in virtue of JA.If the set of all polynomial matrices of A over K,denoted as K[A],is a subspace of linear space Kn×n,the decomposition in a direct sum of subspaces of K[JA] and a base of K[JA] are discussed.A decomposition in a direct sum of subspaces of K[A] is introduced,and a base of K[A] is derived.The results show that it is convenient and feasible for solving the base on subspaces of matrix polynomial space over the complex field through using the decomposition in a direct sum of subspaces.更多还原