Geodesic
Intervals of certain classes of Z-matrices
Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 85-93

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Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.
Keywords: interval matrix, M-matrix, N-matrix, N₀-matrix, nonnegativity 
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Kannan, M.; Sivakumar, K. Intervals of certain classes of Z-matrices. Discussiones Mathematicae. General Algebra and Applications, Tome 34 (2014) no. 1, pp. 85-93. http://geodesic.mathdoc.fr/item/DMGAA_2014_34_1_a5/