矩阵m次根的赋范性质  

Unitarily invariant norm of the m-th algebraic root of a matrix

作　　者：李媛媛[1] 李煜[2] 

机构地区：[1]江汉大学数计学院,湖北武汉430056 [2]海军工程大学电子工程学院,湖北武汉430033

出　　处：《周口师范学院学报》2008年第2期11-14,共4页Journal of Zhoukou Normal University

基　　金：安徽省教育厅重点项目(No.2006KJ066A)

摘　　要：考察了矩阵m次根的奇异值不等式和酉不变范数,得出矩阵m次根的赋范性质:任一酉矩阵的非酉根的酉不变范数均大于1.并利用固定点理论解决了特定数域上矩阵的平方根的存在性和唯一性问题.The m-th algebraic root of a matrix is considered. Relationship between singular values of a complex matrix and its m-tb roots is also investigated. In particular, any unitarily invariant norm of a non-unitary algebraic root of unitary matrix is greater than 1. Based on the analysis of the 2-th order roots of a matrix,the condition for the uniqueness of its solution has been found.

关 键 词：酉不变范数 奇异值 不动点理论 凸函数 收敛 

分 类 号：O151.21[理学—数学]