  We present a number of combinatorial characterizations of K-matrices. This
extends a theorem of Fiedler and Ptak on linear-algebraic characterizations of
K-matrices to the setting of oriented matroids. Our proof is elementary and
simplifies the original proof substantially by exploiting the duality of
oriented matroids. As an application, we show that a simple principal pivot
method applied to the linear complementarity problems with K-matrices converges
very quickly, by a purely combinatorial argument.
