The inverse, rank and product of tensors

In this paper, we give some basic properties for the left (right) inverse, rank and product of tensors. The existence of order 2 left (right) inverses of tensors is characterized. We obtain some equalities and inequalities on the tensor rank. We also show that the rank of a uniform hypergraph is independent of the ordering of its vertices, and the Laplacian tensor and the signless Laplacian tensor have the same rank for odd-bipartite even uniform hypergraphs.