电路中网络矩阵之间关系的拓扑证明

The Relations between the Network Matrixes in Circuit by Topology

在图论中,网络拓扑结构关系可以用关联矩阵A,或基本回路矩阵B,或基本割集C来表示。这三个矩阵之间的关系为ABT=0及BCT=0。相关的电路教材对此关系进行了数学证明。本文通过网络的拓扑结构关系来证明这三个网络矩阵间的关系,相对于数学原理的方法,能够反映出矩阵间内部的逻辑联系,并在证明过程中,提出一些有关网络矩阵的补充定理,完善网络图论的知识体系。

In the graph theory, the structure relations of topology in network can be shown and replaced by incidence matrix A, fundamental circuit matrix B or the fundamental cut-set matrix C. Their relations are AB^T=0 and BC^T =0. And the relations have been demonstrated by the mathematical theory in relevant textbooks. In this paper, the relations are proved with the structure relations of topology in network. And this method can show the intrinsic logic relations in comparison with the method of mathematical theory. In the demonstrating process, some complementary theories about the network matrix are provided, which increase the knowledge about the graph theory in network.