Geodesic
New nonsingularity conditions for general matrices and the associated eigenvalue inclusion sets
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVIII, Tome 439 (2015), pp. 128-144

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The paper suggests generalizations of some known sufficient nonsingularity conditions for matrices with constant principal diagonal and the corresponding eigenvalue inclusion sets to the cases of arbitrary matrices and matrices with nonzero diagonal entries. 
@article{ZNSL_2015_439_a11,
     author = {L. Yu. Kolotilina},
     title = {New nonsingularity conditions for general matrices and the associated eigenvalue inclusion sets},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {128--144},
     publisher = {mathdoc},
     volume = {439},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_439_a11/}
}
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L. Yu. Kolotilina. New nonsingularity conditions for general matrices and the associated eigenvalue inclusion sets. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVIII, Tome 439 (2015), pp. 128-144. http://geodesic.mathdoc.fr/item/ZNSL_2015_439_a11/