Some new inequalities for nonnegative matrices involving Schur product

Abstract

<abstract> <p>In this study, we focused on the spectral radius of the Schur product. Two new types of the upper bound of $ \rho \left({M \circ N} \right) $, which is the spectral radius of the Schur product of two matrices $ M, N $ with nonnegative elements, were established using the Hölder inequality and eigenvalue inclusion theorem. In addition, the obtained new type upper bounds were compared with the classical conclusions. Numerical examples demonstrated that the new type of upper formulas improved the result of Johnson and Horn effectively in some cases, and were sharper than other existing results.</p> </abstract>