Some inequalities for sector matrices

. Two new inequalities are proved for sector matrices. The fi rst one complements a recent result in [Oper. Matrices, 8 (2014) 1143–1148]; the second one is an analogue of the AM-GM inequality, where the geometric mean for two sector matrices was introduced in [Linear Multilinear Algebra 63 (2015) 296-301]. As an application of the second inequality, we present similar inequalities for singular values or norms.