Interval hulls of N-matrices and almost P-matrices

We establish a characterization of almost P-matrices via sign non-reversal property. In this we are inspired by the analogous results for N-matrices. Next, interval hull two m×n matrices A=(aij) and B=(bij), denoted I(A,B), is collection all C∈Rn×n such that each cij convex combination aij bij. Using property, identify finite subset I(A,B) determines if in N-matrices/almost P-matrices. This provides test an entire class simultaneously to be also semipositive minimally matrices. These characterizations may considered similar spirit Białas–Garloff [1] Rohn–Rex [16], positive definite Rohn [15].