The decomposition of higher-order joint cumulant tensors of spatio-temporal data sets is useful in analyzing multi-variate non-Gaussian statistics with a wide variety of applications (e.g. anomaly detection, independent component analysis, ...

We establish a new extremal property of the classical Chebyshev polynomials in the context of best rank-one approximation of tensors. We also give some necessary conditions for a tensor to be a minimizer of the ratio of spectral and Frobenius norms.

A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such as apolarity ...

In this paper we introduce three new classes of nonnegative forms (or equivalently, symmetric tensors) and their extensions. The newly identified nonnegative symmetric tensors constitute distinctive convex cones in the space of general symmetric tensors (...

We give sufficient conditions on a symmetric tensor $\mathcal{S}\in\mathrm{S}^d\mathbb{F}^n$ to satisfy the following equality: the symmetric rank of $\mathcal{S}$, denoted as $\mathrm{srank\;}\mathcal{S}$, is equal to the rank of $\mathcal{S}$, denoted as $...

This paper studies how to compute all real eigenvalues, associated to real eigenvectors, of a symmetric tensor. As is well known, the largest or smallest eigenvalue can be found by solving a polynomial optimization problem, while the other middle ones ...

We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given ...

We introduce a new method for visualizing symmetric tensor fields. The technique produces images and animations reminiscent of line integral convolution (LIC). The technique is also slightly related to hyperstreamlines in that it is used to visualize ...

Visualizing second-order 3D tensor fields continue to be a challenging task. Although there are several algorithms that have been presented, no single algorithm by itself is sufficient for the analysis because of the complex nature of tensor fields. In ...

We consider the asymptotics of certain symmetric k-tensors, the vector analogue of sample moments for i.i.d. random variables. The limiting distribution is operator stable as an element of the vector space of real symmetric k-tensors.