复数域上矩阵多项式空间的基及其子空间的直和分解  

Base and decomposition in a direct sum of subspaces of matrix polynomial space over complex field

作　　者：李红武[1] 王骁力[1] 

机构地区：[1]南阳师范学院数学与统计学院,河南南阳473061

出　　处：《辽宁工程技术大学学报（自然科学版）》2013年第9期1282-1287,共6页Journal of Liaoning Technical University (Natural Science)

基　　金：河南省自然科学基金资助项目(102300410184)

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.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.

关 键 词：复数域 幂零矩阵 同构映射 基 最小多项式 子空间 直和分解 Jordon标准形 

分 类 号：O151.21[理学—数学]