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Findings by M. L. Lyra, S. Mayboroda and M. Filoche relate invertibility andpositivity of a class of discrete Schr\"odinger matrices with the existence ofthe "Landscape Function", which provides an upper bound on all eigenvectorssimultaneously. Their argument is based on the variational principles. Weconsider an alternative method of proving these results, based on the powerseries expansion, and demonstrate that it naturally extends the originalfindings to the case of long range operators. The method of proof by powerseries expansion can also be employed in other scenarios, such as higherdimensional lattices.

Landscape Theory for Schr\"odinger Operators with General Hopping Terms on a Finite Lattice