矩阵向量空间上线性变换的对角化  

The Diagonal Matrix Representation of Linear Transformations On Linear Space of Matrices

作　　者：汪一聪[1] 汪立民[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《五邑大学学报（自然科学版）》2012年第1期15-19,24,共6页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(No.10901134)

摘　　要：由矩阵A定义了n阶矩阵空间Mn(F)上的若干线性变换φA,研究了其线性变化的对角化问题:在A可以对角化的前提下,利用A的特征根与特征向量得到了φA的特征根和特征向量,进而得出φA可以对角化.用A的互异特征根的重数得到了KerφA的维数和范围,用φA的特征向量得到了KerφA的基.Several linear transformations on linear space of matrices Mn（F） are defined by Matrix A and the problem whether these linear transformations have a diagonal matrix representation is investigated in this paper. Under the conditions that A is similar to a diagonal matrix, the eigenvalues and eigenvectors of these linear transformations are acquired by means of the eigcnvalnes and eigenvectors of A. And then the conclusion that these linear transformations have a diagonal matrix representation is obtained. In the meantime, the kernels of these linear transformations as subspaces are investigated by means of the eigenvalues and eigenvectors of A. The dimensions of these subspaces are derived by some of the distinct eigenvalues of A, and the bases of these subspaces are given.

关 键 词：对角化 特征根 特征向量 核空间 

分 类 号：O151.2[理学—数学]