五邑大学学报：自然科学版
五邑大學學報：自然科學版
오읍대학학보：자연과학판
Journal of Wuyi University(Natural Science Edition)
2012年
1期
15-19,24
,共6页
对角化%特征根%特征向量%核空间
對角化%特徵根%特徵嚮量%覈空間
대각화%특정근%특정향량%핵공간
diagonal matrix representation%eigenvalue%eigenvector%kernel space
由矩阵A定义了刀阶矩阵空间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．
由矩陣A定義瞭刀階矩陣空間Mn（F）上的若榦線性變換φA，研究瞭其線性變化的對角化問題：在A可以對角化的前提下，利用A的特徵根與特徵嚮量得到瞭φA的特徵根和特徵嚮量。進而得齣φA可以對角化．用A的互異特徵根的重數得到瞭KerφA的維數和範圍。用φA的特徵嚮量得到瞭KerφA的基．
유구진A정의료도계구진공간Mn（F）상적약간선성변환φA，연구료기선성변화적대각화문제：재A가이대각화적전제하，이용A적특정근여특정향량득도료φA적특정근화특정향량。진이득출φA가이대각화．용A적호이특정근적중수득도료KerφA적유수화범위。용φA적특정향량득도료KerφA적기．
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.
