The algebraic matroid of a Hadamard product of linear spaces and a new proof of Laman's Theorem

Abstract

Using tropical geometry, we show how a construction of Edmonds and Rota that associates a matroid to a submodular function can be used to give a description of the algebraic matroid underlying a Hadamard product of two linear spaces in terms of the matroids underlying each linear space. An immediate consequence of our main result is Laman's Theorem from rigidity theory.