Singular value decomposition in multidimensional arrays

In this paper, an attempt is made to extend the method of singular value decomposition (SVD) to multidimensional (m-D) arrays (tensors). For the sake of brevity the whole study refers to a 3-D array. The 3-D array is transformed to a 2-D array by unifying two dimensions into one. Then, the SVD method is applied to this 2-D array. Afterwards, the unified dimensions are separated and we apply new SVDs. Finally, decomposition of the 3-D array into three dimensions is achieved. An example showing the effectiveness of the method is also presented.