Loss minimizing generator dispatch profiles for power systems are usually derived using optimization techniques. However, by partitioning and manipulating the Ybus matrix, it is possible to derive the KGL matrix, which can be used to analytically determine a loss minimizing dispatch for generators. This letter draws on recent research on the characterization of transmission system losses to demonstrate how the KGL matrix achieves this impressive function. A new proof of the observed zero row summation property of the YGGM matrix is provided to this end.