Eigenvectors of tensors and algorithms for Waring decomposition

The E-Eigenvectors of Tensors

We first show that the eigenvector of a tensor is well-defined. The differences between the eigenvectors of a tensor and its E-eigenvectors are the eigenvectors on the nonsingular projective variety S = {x ∈ P | n

Group Comparison of Eigenvalues and Eigenvectors of Diffusion Tensors

Diffusion tensor imaging (DTI) data differ from most medical images in that values at each voxel are not scalars, but 3×3 symmetric positive definite matrices called diffusion tensors (DTs). The anatomic characteristics of the tissue at each voxel are reflected by the DT eigenvalues and eigenvectors. In this article we consider the problem of testing whether the means of two groups of DT images...

The Eigen-Decomposition: Eigenvalues and Eigenvectors

Eigenvectors and eigenvalues are numbers and vectors associated to square matrices, and together they provide the eigen-decomposition of a matrix which analyzes the structure of this matrix. Even though the eigen-decomposition does not exist for all square matrices, it has a particularly simple expression for a class of matrices often used in multivariate analysis such as correlation, covarianc...

Multilinear Singular Value Decomposition for Structured Tensors

The Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...

Biconjugate Decomposition Using ABS Algorithms