Special H-matrices and their Schur and diagonal-Schur complements

It is well known, see [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246-251 [2]; J. Liu, J. Li, Z. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Alg. Appl. 428 (2008) 1009-1030] [14], that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant, as well as its diagonal-Schur complement. Also, if a matrix is an H-matrix, then its Schur complement and diagonal-Schur complement are H-matrices, too, see [J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Alg. Appl. 389 (2004) 365-380] [13]. Recent research, see [J. Liu, Y. Huang, F. Zhang, The Schur complements of generalized doubly diagonally dominant matrices, Linear Alg. Appl. 378 (2004) 231-244 [12]; J. Liu, J. Li, Z. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Alg. Appl. 428 (2008) 1009-1030] [14], showed that the similar statements hold for some special subclasses of H-matrices. The aim of this paper is to give more invariance results of this type, and simplified proofs for some already known results, by using scaling approach. (C) 2008 Elsevier Inc. All rights reserved.