Abstract:
The paper suggests sufficient nonsingularity conditions for matrices in terms of certain determinantal relations of diagonal dominance type, which improve and generalize some known results. These conditions are used to describe new eigenvalue inclusion sets and to derive new two-sided bounds on the determinants of matrices satisfying them. Bibl. 8 titles.
Key words and phrases:nonsingularity, Cramer's rule, diagonal dominance, minors, structured matrices, Gerschgorin's theorem, the Ostrowski–Brauer theorem, eigenvalue inclusion sets, bounds for determinants.
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