2001•Journal of Hefei University of TechnologyRequires access

Necessary and sufficient conditions of generalized strictly diagonally dominant matrices and nonsingular M-matrices

Qingwei Guo

Abstract

Generalized strictly diagonally dominant matrices and nonsingular M-matrices are two kinds of important matrices. In this paper the necessary and sufficient (NS) condition of real square matrix(RSM) to be a generalized strictly diagonally dominant matrix and the NS condition of the RSM′s comparison matrix to be a nonsingular M-matrix are given.A simple and practicable method of judging generalized strictly diagonally dominant matrices and nonsingular M-matrices is introduced. When this method is adopted,only a non-homogeneous linear equation is needed to solve.

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Key concepts: Diagonally dominant matrix, Invertible matrix, Mathematics, Matrix (chemical analysis), Pure mathematics, Diagonal, Square matrix, Combinatorics