Geodesic
A~theorem on $M$-matrices and its extensions
Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 235-246

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In this paper we consider a useful condition for the positivity of the principal minors of a real matrix with nonnegative elements off the diagonal. This condition is useful for proving the convexity of certain sets in $n$-dimensional space, naturally connected with such matrices. Our result also yields a condition for the nonsingularity of a matrix with arbitrary (complex) elements, unifying conditions of Hadamard and Fidler. 
@article{MZM_1973_13_2_a7,
     author = {V. L. Stefanyuk},
     title = {A~theorem on $M$-matrices and its extensions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {235--246},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a7/}
}
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V. L. Stefanyuk. A~theorem on $M$-matrices and its extensions. Matematičeskie zametki, Tome 13 (1973) no. 2, pp. 235-246. http://geodesic.mathdoc.fr/item/MZM_1973_13_2_a7/