This paper presents a multilinear generalization of the singular value decomposition (SVD), known as higher-order singular value decomposition (HOSVD). The authors analyze the properties of HOSVD, including its relationship to the matrix SVD, its uniqueness, and its connection to the eigenvalue decomposition. They also investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors. The paper discusses the application of HOSVD in signal processing, particularly in the context of higher-order statistics (HOS), where it is used for source separation, blind identification of linear filters, and other tasks. The authors also describe the mathematical framework of HOSVD, including the definition of the n-mode singular values and vectors, the properties of the decomposition, and the conditions under which it is unique. The paper concludes with a discussion of the computational aspects of HOSVD, including how it can be used to approximate higher-order tensors and how it relates to the matrix SVD. The authors emphasize that HOSVD provides a powerful tool for analyzing and processing higher-order tensors in a wide range of applications, including signal processing, statistics, and data analysis.This paper presents a multilinear generalization of the singular value decomposition (SVD), known as higher-order singular value decomposition (HOSVD). The authors analyze the properties of HOSVD, including its relationship to the matrix SVD, its uniqueness, and its connection to the eigenvalue decomposition. They also investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors. The paper discusses the application of HOSVD in signal processing, particularly in the context of higher-order statistics (HOS), where it is used for source separation, blind identification of linear filters, and other tasks. The authors also describe the mathematical framework of HOSVD, including the definition of the n-mode singular values and vectors, the properties of the decomposition, and the conditions under which it is unique. The paper concludes with a discussion of the computational aspects of HOSVD, including how it can be used to approximate higher-order tensors and how it relates to the matrix SVD. The authors emphasize that HOSVD provides a powerful tool for analyzing and processing higher-order tensors in a wide range of applications, including signal processing, statistics, and data analysis.