关于k-广义Hermite矩阵的研究  

Research of k-generalized Hermite matrix

作　　者：袁晖坪[1] 

机构地区：[1]重庆工商大学数学与统计学院,电子商务及供应链系统重庆市重点实验室,重庆400067

出　　处：《东北师大学报（自然科学版）》2012年第2期5-8,共4页Journal of Northeast Normal University(Natural Science Edition)

基　　金：重庆市自然科学基金资助项目(CSTS 2005BB 0243);重庆市教委科技基金资助项目(KJ0707023)

摘　　要：给出了k-广义Hermite矩阵的概念,探讨了它的性质及其与Hermite矩阵、酉矩阵、Hamilton矩阵的广义逆矩阵之间的联系,取得了许多新的结果,推广了酉矩阵、Hermite矩阵及R.D.Hill的广义次对称矩阵间的相应结果,特别是将正交阵的广义Cayley分解推广到了k-广义酉矩阵和k-广义Hermite矩阵上,从而将各类Hermite矩阵及广义逆矩阵统一起来.The author stated concepts of k-generalized Hermite matrix,its properties and relations with H ermite matrix, unitary matrix, Hamilton matrix and generalized inverse matrix were discussed, with many new results obtained. The corresponding results among unitary matrix, Hermite matrix and generalized symmetric matrix, especially the Cayley decomposition of orthogonal matrix to k- generalized unitary matrix and k-generalized Hermite matrix were extended,and unifying various kinds of the Hermite matrix and generalized inverse matrix.

关 键 词：k-广义Hermite矩阵 酉矩阵 HERMITE矩阵 广义逆矩阵 辛矩阵 

分 类 号：O151.21[理学—数学]