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《Journal of Wuyi University(Natural Science Edition)》 2012-01
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The Diagonal Matrix Representation of Linear Transformations On Linear Space of Matrices

WANG Yi-cong,WANG Li-ming(School of Mathematical Science,South China Normal University,Guangzhou 510631,China)  
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 eigcnvalues 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.
【Fund】: 国家自然科学基金资助项目(No.10901134)
【CateGory Index】: O151.21
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