Kirchoff's matrix of an electrical network

We may reinterpret these equations with Kirchoff's matrix $K = (k_{i j})$

k_{i j} = {\begin{cases} - \sum_{e : i - j} \frac{1}{R_{e}} & i \neq j \\ \sum_{e connected to i} \frac{1}{R_{e}} & i = j \end{cases}

Properties