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I am trying to create a computer program to compute the equivalent resistance over any points on any rectangular set of resistors (all with a resistance of 1 ohm). It seems that the resistance distance matrix is exactly what I need. I understand how to compute the inverse and what a Laplacian matrix is, but what is the difference between $\Gamma_{ii}$, $\Gamma_{jj}$, and $\Gamma_{ij}$ in $\Omega_{ij} = \Gamma_{ii}$ + $\Gamma_{jj} - 2\Gamma_{ij}$?

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$\Gamma_{ii}$ is the $i$-th entry on the diagonal of $\Gamma = L^+ = (D-A)^+$, $\Gamma_{jj}$ is the $j$-th entry, and $\Gamma_{ij}$ is the entry located at row $i$, column $j$. Thus $\Omega_{ij}$ is a scalar, but you could assemble all such values into a matrix $\Omega$ that gives the resistances between all pairs of vertices.

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