改进的AHP中反对称阵的扰动矩阵的性质

The properties of the perturbation matrices of antisymmetric matrices in the improved AHP

给出了标准形概念 ,定义了标准形 ,并证明在改进的AHP中 ,反对称阵的扰动矩阵集合和标准形集合相等 ,任一反对称阵均可惟一分解为一个传递阵和一个标准形的和 .

In this paper,the standard matrices are defined,the fact that the set of the perturbation matrices of antisymmetric matrices is equal to the set of standard matrices is proved,and every antisymmetric matrix can be uniquely decomposed into the sum of a transitive matrix and a standard matrix.