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=1,..., xj ∈Cn}. Here Cn 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 n∑j=1νj≠ 0. Next, we study some properties of the y-numerical radius of matrices and vectors with non-negative entries.
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