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Combinatorial characterizations of K-matrices

Foniok, J and Fukuda, K and Klaus, L (2011) Combinatorial characterizations of K-matrices. Linear Algebra and Its Applications, 434. ISSN 0024-3795

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Abstract

We present a number of combinatorial characterizations of K-matrices. This extends a theorem of Fiedler and Pt´ak 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.

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