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. Bibliography: 8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 382, 2010, pp. 104–124.
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Kolotilina, L.Y. On determinantal diagonal dominance conditions. J Math Sci 176, 57–67 (2011). https://doi.org/10.1007/s10958-011-0393-8
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DOI: https://doi.org/10.1007/s10958-011-0393-8