Combinatorial characterizations of \(K\)-matrices (Q609481)

The paper provides a number of combinatorial characterizations of a \(K\)-matrix. This concept refers to a square real matrix which is simultaneously a \(P\)-matrix (i.e., the principal minors are positive) and a \(Z\)-matrix (i.e., the off-diagonal entries are nonpositive). The authors extend a theorem of \textit{M. Fiedler} and \textit{V. Ptak} [Czech. Math. J. 12(87), 382--400 (1962; Zbl 0131.24806)] on linear-algebraic characterizations of \(K\)-matrices to the setting of oriented matroids.