Characterization, perturbation, and interval property of certain sign regular matrices

The class of square matrices order n having a negative determinant and all their minors up to n−1 nonnegative is considered. A characterization these presented which provides an easy test based on the Cauchon algorithm for recognition. Furthermore, maximum allowable perturbation entry in position (2,2) such that perturbed matrix remains this given. Finally, it shown lying between two with respect checkerboard ordering are contained class, too.