摘要： For a complex matrix A=[aij]i,j=1n, let W(A) be its numerical range, and let G(A) be the convex hull of ⋃i=1n{z∈C:|z-aii|⩽(∑i≠j(|aij|+|aji|))/2} and G′(A)=⋂{G(U*AU):Un-by-nunitary}.It is known that W(A) is always contained in G(A) and hence in G′(A). In this paper, we consider conditions for W(A) to be equal to G(A) or G′(A). We show that if W(A)=G′(A), then the boundary of W(A) consists only of circular arcs and line segments. If, moreover, A is unitarily irreducible, then W(A) is a circular disc. (Almost) complete characterizations of 2-by-2 and 3-by-3 matrices A for which W(A)=G′(A) are obtained. We also give criteria for the equality of W(A) and G(A). In particular, such A’s among the permutationally irreducible ones must have even sizes. We also characterize those A’s with size 2 or 4 which satisfy W(A)=G(A). 出版者： Elsevier Inc 出版日期： 2013-02-01 出處： Linear algebra and its applications, 2013-02, Vol.438 (3), p.1170-1192 資源來源： Elsevier ScienceDirect Journals Complete - Autoholdings 版權： 2012 識別號： ISSN: 0024-3795 識別號： EISSN: 1873-1856 識別號： DOI: 10.1016/j.laa.2012.09.003
