Positive semidefinite tensors

In the era of big data, the high-order high-dimensional tensor structure has attracted more and more attention, which further leads to the extensive study on tensor theory, computation and applications. Analogous to the matrix case, the positive semidefinite tensors, which form an important class of tensors, have played an essential role in tensor applications. This paper aims to provide a simple survey of the positive semidefiniteness of tensors and some potential research directions on tensor theory.