关于正规矩阵的判定  

The determining conditions of normal matrices

作　　者：陈惠汝[1] 刘红超[1] 

机构地区：[1]黄冈师范学院数学与信息科学学院,湖北黄冈438000

出　　处：《高师理科学刊》2009年第5期87-89,共3页Journal of Science of Teachers＇College and University

摘　　要：对角矩阵、Hermite矩阵、反Hermite矩阵、酉矩阵、对称矩阵、反对称矩阵、正交矩阵都是正规矩阵,所以正规矩阵作为一个更为广泛的矩阵类,有必要对它的判定条件进一步研究.由正规矩阵的定义、矩阵对角化、特征值与特征向量、矩阵实部和虚部、矩阵分解、谱分解等方面给出了正规矩阵的一些判定条件.Diagonal matrix,hermite matrix,skew-Hermitian matrix,unitary matrix,symmetric matrix,skew-symmetric matrix,orthogonal matrix are normal matrices.Normal matrices so formal as a wider range of matrices,it is necessary to determine the conditions for its further study.The determining conditions of normal matrices was disussed in aspects of definition,matrix diagonalization,eigenvalue and eigenvector,matrix realand and imaginary parts,matrix decomposition and prover vector.

关 键 词：正规矩阵 SCHUR定理 对角化 特征向量 谱分解 

分 类 号：O151.21[理学—数学]