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Let $P_{ij}$ be variables, and let $A \in \mathbb{R}^{n\times n}$ be the matrix defined by $$ A_{ij} = \begin{cases} -P_{ij} & i \neq j,\\ P_{i1} + P_{i2} + \dots + P_{in} & i=j. \end{cases} $$...

Let $(V,E)$ be a finite oriented directed graph, with vertices and edges ordered, and $M$ the $|V|\times |E|$ matrix with entries $$ m_{ve} = \begin{cases} 1 &\text{if $e$ points at $v$}\\ -1 &...