Abstract
The theory of M-matrices provides fundamental tools in the analysis of problems in numerical linear algebra, particularly in the iterative solution of large sparse systems of linear equations. The theory of M-matrices continues to be the underlying theme, whether directly or indirectly, for many recent contributions in numerical linear algebra. This chapter presents a few equivalent conditions for an H-matrix and also discusses the way in which those conditions relate to recent results in literature. It also reviews the concept of generalized column diagonal dominance, strict irreducible diagonal dominance, semi-strict diagonal dominance, and lower semi-strict diagonal dominance.
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