Adjoints and Duals of Matroids Linearly Representable over a Skewfield.

Adjoints and Duals of Matroids Linearly Representable over a Skewweld Abstract Following an approach suggested by B. Lindstrr om we prove that the dual of a matroid representable over a skewweld is itself representable over the same eld. Along the same line we show that any matroid within this class has an adjoint. As an application we derive an adjoint for the dual of the Non-Pappus-Matroid. Furthermore, we reprove a result by Alfter and Hochstt attler concerning the existence of an adjoint for a certain eight point connguration and show that this connguration is linearly representable over a eld if and only if the eld is skew.