Bounds on the spectral sparsification of symmetric and off-diagonal nonnegative real matrices

Abstract

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