一个n阶符号模式矩阵A称为是谱任意的,如果对任意的实系数n次首1多项式r(x),在A的定性矩阵类Q(A)中至少存在一个实矩阵B,使得B的特征多项式是r(x).文中证明了当n为奇数时n阶谱任意符号模式矩阵是存在的.
A sign pattern matrix A of order n is a spectrally arbitrary pattern (SAP) if given any monic polynomial r(x) of order n with real coefficients, there exists a real matrix B in the sign pattern class of A such that the characteristic polynomial of B is r(x). In this paper, we prove that there exists a spectrally arbitrary pattern of order n when n is odd.