关于矩阵per-相合数值域的形状

On the Shape of the per-Congruence Numerical Range of a Matrix

n阶复方阵A的per-相合数值域是指集合(?)。本文提出猜想:当n>2时,在复平面上为中心在原点的圆面,同时对A为对称或反对称矩阵时给出了肯定的回答。

For A∈C_(nxn), let R 1/n(A)={per(U^T AU)|U∈U_n}. The paper conjectures that R 1/n(A) is a disk centered at the origin in the complex plane provided n>2 and the affirmative answer for A∈S_n or A∈K_n is obtained.