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2003•Journal of Xiamen UniversityRequires access

α-Double Diagonally Dominant Matrices

Linzhang Lu

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Abstract

Li Bishan and Tsatsomeros gave the definition of doubly diagonally dominant matrix and presented some necessary and sufficient conditions for an irreducible doubly diagonally dominant matrix to be a sigular matrix or not to be an H-matrix. In this paper,we present some necessary and sufficient conditions in terms of the directed graph for an irreducible a-doubly diagonally dominant matrix to be a singular matrix or not to be an H-matrix,and generalize the related results of Li and Tsatsomeros'.

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What this paper is about

Li Bishan and Tsatsomeros gave the definition of doubly diagonally dominant matrix and presented some necessary and sufficient conditions for an irreducible doubly diagonally dominant matrix to be a sigular matrix or not to be an H-matrix. In this paper,we present some necessary and sufficient conditions in terms of the directed graph for an irreducible a-doubly diagonally dominant matrix to be a singular matrix or not to be an H-matrix,and generalize the related results of Li and Tsatsomeros'.

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Available abstract

Li Bishan and Tsatsomeros gave the definition of doubly diagonally dominant matrix and presented some necessary and sufficient conditions for an irreducible doubly diagonally dominant matrix to be a sigular matrix or not to be an H-matrix. In this paper,we present some necessary and sufficient conditions in terms of the directed graph for an irreducible a-doubly diagonally dominant matrix to be a singular matrix or not to be an H-matrix,and generalize the related results of Li and Tsatsomeros'.

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

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