一个新的极小谱任意复符号模式矩阵

A new matrix of minimally spectrally arbitrary complex sign patterns

设S是n阶复符号模式矩阵,若对于任意一个n阶首一复系数多项式f(x),都存在一个复矩阵B∈Q_c(S),使得该矩阵的特征多项式为f(x),则称复符号模式矩阵S是谱任意的。运用中值定理来实现幂零,并用幂零—雅可比方法证明了一个新的复符号模式矩阵是极小谱任意的。

An n x n complex sign pattern matrix S is said to be spectrally arbitrary if for every monic n th degree polynomial f（x） with complex coefficients, there is a complex sign pattern matrix B∈Qc（S） such that its characteristic polynomial is f（x）. Nilpotent realization is given by using the intermediate value theorem. It is proven that a new complex sign pattern matrix is minimally spectrally arbitrary by the Nil- potent-Jacobian method.