关于非负矩阵的反特征值问题

应用多项式的伙伴矩阵, 对于任意复数~$\lambda, $ 构造出了三阶非负方阵, 使~$\lambda$~为其一特征值, 并证明所给出的是满足条件的含零元素最多的矩阵.

Inverse eigenvalue problem for nonnegative matrices

For any given complex number $\lambda$, this paper proved that there exists a 3 by 3 nonnegative matrix \textbf{\emph{A}} with at least 4 zero entries such that $\lambda$ is an eigenvalue of \textbf{\emph{A}}. The number 4 of zero entries here is the largest possible.