电网络基本矩阵转置等式证明

The Proof of Transposed Equations of Basic Electric Network Matrices

关联矩阵A,基本回路矩阵B,基本割集C矩阵是电网络拓扑图中的基本矩阵。本文通过对电网络拓扑图的节点、支路、回路、割集的拓扑结构的讨论,证明了A,B,C矩阵的转置恒等式。其中,在对B,C矩阵转置恒等式的证明中利用了连通片的结构,并详细阐述了电网络转置恒等式在电网络拓扑图中的表现形式。

Incidence matrix A,fundamental circuitmatrix B andfundamental cut-set matrix C are three most basic matrices in the electric topology network.In order to prove the transposed identities related to A,B,C matrix,this article discusses the topological structure of node,branch,loop and cut-set in the network.During the proof of the identities of B and C matrix,the connected component structure is used to clarify the form of the electric network identities in thetopological graph.