Grassmann Tensors and their applications in geometry

In this paper, we introduce the Grassmann tensor by tensor product of vectors and some basic terminology in tensor theory. Some basic properties of the Grassmann tensors are investigated and the tensor language is used to rewrite some relations and correspondences in the mutliview geometry. Finally we show that a polytope in the Euclidean space ${\mathbb{R}}^n$ can also be concisely expressed as the Grassmann tensor generated by its vertices.