Bounds on the Spectral Sparsification of Symmetric and Off-Diagonal Nonnegative Real Matrices

09/23/2020

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by   Sergio Mercado, et al.

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We say that a square real matrix M is off-diagonal nonnegative if and only if all entries outside its diagonal are nonnegative real numbers. In this note we show that for any off-diagonal nonnegative symmetric matrix M, there exists a nonnegative symmetric matrix M which is sparse and close in spectrum to M.