Characterization, perturbation, and interval property of certain sign regular matrices (Q2228520)

In this nicely written paper, the authors consider the class of sign regular matrices of order \(n\) having a negative determinant and nonnegative minors up to order \(n-1\) (\(NsTN^-\) matrices), and apply the Cauchon algorithm. The Cauchon algorithm is used to provide a new characterization and further properties of the \(NsTN^-\) matrices, to derive new necessary and sufficient conditions for a matrix to be \(NsTN^-\). They show that these matrices possess the interval property, i.e., all matrices lying between two such matrices with respect to the checkerboard ordering are also \(NsTN^-\) matrices. Moreover, the maximum allowable perturbation of the most critical entry in position (2,2) of an \(NsTN^-\) matrix such that the perturbed matrix remains in this class is presented.