三次幂等矩阵与酉矩阵线性组合的研究  

Some researches of linear combinations of two tripotents and unitary matrices

作　　者：任芳国[1] 王林娥[1] 秦晓燕[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《纺织高校基础科学学报》2013年第3期313-317,共5页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11171201);陕西省自然科学基金资助项目(2011JM1007)

摘　　要：利用代数的方法,对给定的两个非零三次幂等矩阵P1,P2和酉矩阵U1,U2,讨论了线性组合P=c1P1+c2P2保持三次幂等性系数所满足的充要条件.给出了使线性组合U=c1U1+c2U2保持酉性时系数所满足的充分条件,其中c1,c2为非零的复数.利用矩阵极分解给出酉矩阵线性组合的性质刻画.Given two nonzero tripotent matrices P1 ,P2 and unitary matrices U1 ,U2 ,tripotency and unility problems of linear combinations that were preserved were discused by using algebra method .Some suffi-cient and necessary conditions of c1 P1 ＋ c2 P2 were obtained .And some sufficient condition of c1U2 ＋ c2U2 for a unitary matrix were given .The property of linear combinations of unitary matrices was character-ized .

关 键 词：三次幂等矩阵 酉矩阵 压缩矩阵 极分解 

分 类 号：O152.21[理学—数学]