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.
出处
《周口师范学院学报》
CAS
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)
关键词
酉不变范数
奇异值
不动点理论
凸函数
收敛
unitarily invariant norm
singular value
fixed point theorem
quad convex function
quad convergence
