Determinant And Rank Of Symmetric Tensor

Tensor is a higher-order extension of matrix. With the development of technology, the traditional matrix theory reflects the limitations of their data processing. Now in the multi-dimensional data flow techniques, such as Internet chat rooms, communications data, complex fluorescence excitation and emission measurements, as well as physics, chemistry, medicine, etc, tensor plays a important role in this applications. In this paper, we introduce the determinant and rank of high-order tensor and extend some properties of matrix to tensor.