Algorithmic detection and construction of N-matrices (Q2185838)

A real \(n \times n\) matrix is called an N-matrix if all the principal minors of \(A\) are negative. N-matrices form an important matrix class due their connection to univalence theory and the linear complementarity problem. Here, the authors provide an \(\mathcal{O}(2^n)\) test to detect whether or not a given matrix is an N-matrix. A characterization of N-matrices is then presented. This leads to their recursive construction.