On Nekrasov matrices Original Research Article

In this paper we investigate nonsingularity of a generalized Nekrasov matrix and present some sufficient conditions for this matrix to be nonsingular on one hand. On the other hand, we also establish some sufficient and necessary conditions for a diagonally dominant matrix or a generalized Nekrasov matrix to be a generalized diagonally dominant matrix. All results in this presentation improve and generalize the corresponding results of Huang (T. Huang, Linear Algebra Appl. 225 (1995) 237) and Szulc (T. Szulc, Linear Algebra Appl. 225 (1995) 221).