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A Simple Criterion for Nonsingular H-Matrix

Wang Xiaoo

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Abstract

Let A=(aij)∈Cn×n,if there existsα∈(0,1)which can make|aii|≥Rαi(A)S1-αi(A)be right for ■i∈N={1,2,…,N},then Ais called aαchain diagonally dominant matrix.By using concepts and properties of theαchain diagonally dominant matrices;irreducibleαchain diagonally dominant matrices and generalized strictlyαchain diagonally dominant matrices,some sufficient conditions for a matrix to be a nonsingular H-matrix were given.The results obtained improve the known corresponding results.At last a numerical example is given for illustrating advantage of result.

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What this paper is about

Let A=(aij)∈Cn×n,if there existsα∈(0,1)which can make|aii|≥Rαi(A)S1-αi(A)be right for ■i∈N={1,2,…,N},then Ais called aαchain diagonally dominant matrix.By using concepts and properties of theαchain diagonally dominant matrices;irreducibleαchain diagonally dominant matrices and generalized strictlyαchain diagonally dominant matrices,some sufficient conditions for a matrix to be a nonsingular H-matrix were given.The results obtained improve the known corresponding results.At last a numerical example is given for illustrating advantage of result.

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Available abstract

Let A=(aij)∈Cn×n,if there existsα∈(0,1)which can make|aii|≥Rαi(A)S1-αi(A)be right for ■i∈N={1,2,…,N},then Ais called aαchain diagonally dominant matrix.By using concepts and properties of theαchain diagonally dominant matrices;irreducibleαchain diagonally dominant matrices and generalized strictlyαchain diagonally dominant matrices,some sufficient conditions for a matrix to be a nonsingular H-matrix were given.The results obtained improve the known corresponding results.At last a numerical example is given for illustrating advantage of result.

Key concepts: Diagonally dominant matrix, Invertible matrix, Mathematics, Matrix (chemical analysis), Simple (philosophy), Combinatorics, M-matrix, Diagonal

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