Geodesic
On determinantal diagonal dominance conditions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 104-124

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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. 
@article{ZNSL_2010_382_a8,
     author = {L. Yu. Kolotilina},
     title = {On determinantal diagonal dominance conditions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {104--124},
     publisher = {mathdoc},
     volume = {382},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a8/}
}
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L. Yu. Kolotilina. On determinantal diagonal dominance conditions. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 104-124. http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a8/