摘要
Given an n×n complex matrix A and an n-dimensional complex vector y=(ν1 , ··· , νn ), the y-numerical radius of A is the nonnegative quantity ry(A)=max{n∑j=1ν*jAx︱:Axj︱: x*jxj=1,xj ∈Cn}.Here Cn is an n-dimensional linear space overthe complex field C. For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}.We show that ry is a generalized matrix norm if and only ifn∑j=1νj≠ 0.Next, we study some properties of the y-numerical radius of matrices andvectors with non-negative entries.
Given an n × n complex matrix A and an n-dimensional complex vector y = （v1, ..., vn）, the y-numerical radius of A is the nonnegative quantity ry（A） = max{｜∑ j=1^nvjxjAxj｜}xjxj=1,xj∈C^n}Here C^n is an n-dimensional linear space over the complex field C. For y = （1,0,…,0） it reduces to the classical radius r（A） =max{｜x^＊Ax｜： x^＊x = 1}. We show that ry is a generalized matrix norm if and only if ∑j=1 ^nvj≠0.Next, we study some properties of tile y-numerical radius of matrices andvectors with non-negative entries.
基金
Foundation item： Supported by the Natural Science Foundation of Hubei Province（B20114410）
