Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 20, 2009, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jan Foniok

A combinatorial characterization of K-matrices

A Z-matrix is a square matrix whose off-diagonal elements are non-positive. A P-matrix is a square matrix whose principal minors are positive. A K-matrix is a matrix that is both a Z-matrix and a P-matrix.

In 1962, Fiedler and Pták listed thirteen equivalent conditions for a Z-matrix to be a K-matrix. Some of them concern the sign structure of some vectros; we generalize these conditions in the context of oriented matroids and prove their equivalence in this purely combinatorial context, using no wild linear algebra.

Our motivation to do this stems from the linear complementarity problem. A by-product of our theorem is another proof that LCP for K-matrices can be solved in linear time even by the drunken pivotter.

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