幂零--中心化方法

The Nilpotent-Centralizer Methods

中文关键词:  复符号模式  Ray模式  谱任意模式  幂零.

英文关键词:complex sign pattern  ray pattern  spectrally arbitrary pattern  nilpotence.

中文摘要:

      一个$n$阶复符号模式(ray模式)${\cal S}$称为是谱任意的,如果对于任意$n$次首1复系数多项式$f(\lambda)$, 在${\cal S}$的复符号模式类(ray模式类)中总存在一个复数矩阵, 使得它的特征多项式是$f(\lambda)$.我们分别推广幂零--中心化方法到谱任意复符号模式和ray模式.我们发现幂零--中心化方法的形式对于符号模式, 复符号模式, ray模式是一致的.

英文摘要:

      An $n \times n$ complex sign pattern (ray pattern) ${\cal S}$ is said to be spectrally arbitrary if for every monic $n$th degree polynomial $f(\lambda)$ with coefficients from $\mathbb{C}$, there is a complex matrix in the complex sign pattern class (ray pattern class) of ${\cal S}$ such that its characteristic polynomial is $f(\lambda)$. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns (sign pattern, complex sign pattern, ray pattern) are the same in form.