Linear Spaces

In this chapter, we start to study the behaviour of linear varieties under Hadamard products. We begin with some useful results about the Hadamard multiplication of linear spaces by a point. Then, we study Hadamard products, and powers, of lines. Successively, we consider Hadamard products of linear spaces. Using Tropical Geometry, we are able to give some insight on the degree and the dimension of such Hadamard products. The last section introduces an important connection between the Hadamard product of two linear spaces and a suitable Segre embedding.