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Doubly diagonally dominant matrices. (English) Zbl 0886.15027

Doubly diagonally dominant matrices are those whose ovals of Cassini do not include the origin. This paper gives necessary and sufficient conditions for irreducible such matrices to be singular or an \(H\)-matrix. It is also shown that Schur complements of such matrices remain doubly diagonal dominant.
Reviewer: F.Uhlig (Auburn)

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
15A09 Theory of matrix inversion and generalized inverses
15A45 Miscellaneous inequalities involving matrices
15B48 Positive matrices and their generalizations; cones of matrices
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