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The construction of the Varchenko matrix for hyperplane arrangements, firstintroduced by Alexandre Varchenko, extends naturally to oriented matroids. Inthis paper, we generalize the theorem of Gao and Zhang by proving that theVarchenko matrix of an oriented matroid has a diagonal form if and only if thepseudohyperplane arrangement corresponding to the oriented matroid is insemigeneral position, i.e. it does not contain a degeneracy.  Furthermore, we show that the Varchenko matrix of a pseudoline arrangementhas a block diagonal form. This also provides an alternative combinatorialproof for the Varchenko matrix determinant formula in dimension two.

Diagonal form of the Varchenko matrices for oriented matroids