主理想环上矩阵可对角化的新判据  

New Diagonalization Condition for Matrices in a Domain of Principal Ideal

作　　者：邓勇[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什市844006

出　　处：《山东农业大学学报（自然科学版）》2015年第4期625-627,共3页Journal of Shandong Agricultural University：Natural Science Edition

基　　金：国家社科基金项目(11XTJ001)

摘　　要：矩阵的对角化问题在矩阵理论中占有重要地位.为将域上矩阵可对角化的结果进行推广,研究了主理想环上矩阵的可对角化问题,获得了主理想环上一类具有最小多项式m(λ)=(λ-α)(λ-β),α≠β的矩阵可对角化的充分必要条件.在此基础上,进一步证明了具有二次最小多项式的两个可对角化矩阵A,B有公共特征向量,当且仅当它们的交换子[A,B]是奇异矩阵.The diagonalization of matrices has an important position in the matrix theory. In order to expand the results for diagonalization of matrices over fields, we discussed the diagonalization of matrices over a domain of principal ideals, and obtained the necessary and sufficient conditions of diagonalization of matrices over a domain of principal ideals with minimal polynomial m(λ)=(λ?α)(λ?β),α≠β. Further, on the basis of the obtained results, the conditions under which the matrices A and B have common eigenvectors if and only if their commutator [A, B] is singular matrix, was proved.

关 键 词：主理想环 对角化 最小多项式 特征向量 交换子 

分 类 号：O151.21[理学—数学] O157.3[理学—基础数学]