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Varchenko defined the Varchenko matrix associated to any real hyperplanearrangement and computed its determinant. In this paper, we show that theVarchenko matrix of a hyperplane arrangement has a diagonal form if and only ifit is semigeneral, i.e., without degeneracy. In the case of semigeneralarrangement, we present an explicit computation of the diagonal form viacombinatorial arguments and matrix operations, thus giving a combinatorialinterpretation of the diagonal entries.

Diagonal Form of the Varchenko Matrices