  The construction of the Varchenko matrix for hyperplane arrangements, first
introduced by Alexandre Varchenko, extends naturally to oriented matroids. In
this paper, we generalize the theorem of Gao and Zhang by proving that the
Varchenko matrix of an oriented matroid has a diagonal form if and only if the
pseudohyperplane arrangement corresponding to the oriented matroid is in
semigeneral position, i.e. it does not contain a degeneracy.
  Furthermore, we show that the Varchenko matrix of a pseudoline arrangement
has a block diagonal form. This also provides an alternative combinatorial
proof for the Varchenko matrix determinant formula in dimension two.
