On the powers of a vectorial matroid – an equivalence relation Original Research Article

Let V be a nonzero vector space over the field image of characteristic zero. Let X be a finite family of nonzero vectors of V. For each aset membership, variantV, we denote by Ma the vectorial matroid of Xunion or logical sum(a). For each image we denote by Ma(k) the kth power of Ma. We define an equivalence relation, πk, on V such that aπkb if and only if the matroids Ma(k) and Mb(k) are on the same set and have the same set of independent sets. We present results on this equivalence relation.