广义酉矩阵与广义Hermite矩阵的一些性质  

Some Properties of Generalized Unitary Matrices and Generalized Hermite Matrices

作　　者：程静[1] 何承源[1] 

机构地区：[1]西华大学数学与计算机学院,成都610039

出　　处：《重庆师范大学学报（自然科学版）》2010年第3期58-59,68,共3页Journal of Chongqing Normal University:Natural Science

基　　金：西华大学应用数学校重点学科(No.ZXD0910-09-1)

摘　　要：主要研究两类重要的、具有特殊性质的矩阵——广义酉矩阵和广义Hermite矩阵。对广义酉矩阵和广义Her-mite矩阵的性质进行了推广,得到几种新的判别广义酉矩阵和广义Hermite矩阵的判别条件:若A∈Cnn相似于一个酉矩阵U,则A是n阶P-广义酉矩阵;已知A可对角化,则A为n阶P-广义酉矩阵的充分必要条件是A相似于一个酉矩阵;若A为广义P-酉矩阵,则A是广义P*-酉矩阵;若A为实矩阵,则A为广义Hermite矩阵;若A为n阶广义P-Hermite矩阵,则A为n阶广义P*-Hermite矩阵。给出了广义酉矩阵的特征值:如果λ≠0是A的特征值,那么1/λ是A*的特征值;当A为实矩阵时,1/λ也是A的特征值。This paper focuses on two types of special matrices ： the generalized unitary matrix and the generalized Hermite matrix. Promoted the nature of these two types of matrices we can obtained several new conditions of these two types of matrices . Such as ： if a matrix A ∈ Cn^n similar to a unitary matrix U, then A is the n-generaliized unitary matrix; if A can be diagonallyzable, then A is a n-generalized unitary matrix the necessary and sufficient condition is A similar to a unitary matrix; if A is a generalized P-unitary matrix, then A is a generalized P ^＊ -unitary matrix ; if a matrix A is a real matrix, then A is a generalized Hermite matrix; if A is a n-order generalized P-Hermite matrix, then A is a n-order generalized P ^＊ -Hermite matrix . Gives the eigenvalues of the generalized unitary matrices： if λ #0 is the eigenvalues of A, then 1/λ is the eigenvalues of A^＊ ; when A is a real matrix, 1/λ is the eigenvalues of A.

关 键 词：广义酉矩阵 广义HERMITE矩阵 性质 条件 

分 类 号：O151.21[理学—数学]