电路分析的观察法和矩阵法的等效证明

回路电流法与节点电压法是电路分析的有效方法，而节点导纳矩阵Y_n，回路阻抗矩阵Z_l，节点源电流向量I_Sn，回路源电压向量U_Sl是在使用这两种方法时定义的矩阵与向量。然而，教材后文在引入两种方法的矩阵形式时，再次对上述矩阵与向量进行了定义。本文利用矩阵展开法，证明了两种定义的等价性，并给出含有耦合电感及受控源时，上述矩阵与向量的计算方法。

The Equivalent Proofs of The Observational Method And The Matrix Method in The Circuit Analysis

Loop current analysis and node voltage analysis are two methods for the circuit analysis. All node admittance matrix Y_n, loop impedance matrix Z_l, node source-current vector I_Sn and vector of loop current U_Sl are defined while using these two methods. However, while the matrix form of these two methods is introduced in the textbook, those matrices and vectors are redefined. This article prove the equivalency of these two definitions by using the matrix expansion method, and then discusses the calculations of the matrix coefficients related to these matrices and vectors while considering the coupled inductance and controlled source in the electric network.