一类符号模式矩阵嵌套蕴含稳定性的刻划

A Characterization of Nested Potential Stability of a Class of Sign Pattern Matrix

设A为n阶符号模式矩阵,若存在与A有相同符号模式的实矩阵B及n阶置换矩阵P,使得C=PTBP的各阶顺序主子式负正相间,则称A是嵌套蕴含稳定的.该文研究一类特殊的符号模式矩阵,给出其嵌套蕴含稳定的完全刻划.

An n×n sign pattern matrix A is nested potentially stable,if there is a real matrix B in which it has same sign pattern with A and a permutation matrix P such that k-th leading principal minor of PTBP signed as（-1）k for all k=1,2,…,n.In this paper,we consider one class of sign pattern matrixes.We characterized its nested potential stability completely.