关于反对称符号模式的若干性质

Several Properties of Anti-Symmetry Sign Pattern

设A是n阶反对称符号模式.利用矩阵理论和组合论的方法刻化了Ak的惯量,给出了符号模式A惯量的若干性质,最后给出了符号模式矩阵A蕴含正交的一个充分必要条件.

Let A be a n-order anti-symmetric sign pattern. After characterizing the inertia of sign pattern A^k by using the methods of matrix theory and combinatorial theory, this paper presents several properties of the inertia of A, and a sufficient and necessary condition under which the sign pattern matrix A is orthogonal.