Tensor decomposition of Toeplitz Jacket matrices for big data processing In this paper, we consider the tensor decomposition (TD) of Toeplitz Jacket (TJ) matrices for big dataprocessing by using the conventional higher order singular value decomposition (HOSVD) algorithm and Tensor train (TT) decomposition. In order to use HOSVD algorithm and TT decomposition, we reshape the given matrix and make it as a tensor. Due to the property of Toeplitz matrices, we use a truncated TJ matrix in stead of given matrix to reduce the complexity of TD. The results verified that the TD of the truncated TJ matrices gains a lower complexity due to smaller size of factor matrices and core tensors.