Tensors (also known as multidimensional arrays or N -way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB’s multidimensional arrays by supporting additional operations such as tensor multiplication...

In this paper, we present the boundedness of solution set of tensor complementarity problem defined by a strictly semi-positive tensor. For strictly semi-positive tensor, we prove that all H+(Z+)-eigenvalues of each principal sub-tensor are positive. We define two new constants associated with H+(Z+)-eigenvalues of a strictly semi-positive tensor. With the help of these two constants, we establ...

We present a visual approach for the exploration of stress tensor fields. Therefore, we introduce the idea of multiple linked views to tensor visualization. In contrast to common tensor visualization methods that only provide a single view to the tensor field, we pursue the idea of providing various perspectives onto the data in attribute and object space. Especially in the context of stress te...

We present the basic concepts of tensor products of vectors spaces, exploiting the special properties of vector spaces as opposed to more general modules: Introduction (1), Basic multilinear algebra (2), Tensor products of vector spaces (3), Tensor products of matrices (4), Inner products on tensor spaces (5), Direct sums and tensor products (6), Background concepts and notation (7), Discussion...

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.

We present three methods of visualizing tensor fields that offer new ways of looking at tensor volumes. All three methods are based on the interaction of simulated light and the tensor field. Conceptually, rays are shot from a certain direction into the tensor volume. These rays are influenced by the surrounding tensor field and bent as they traverse through the volume. The tensor is visualized...

AD is the highly severe part of dementia spectrum and impairs cognitive abilities individuals, bringing economic, societal psychological burdens beyond diseased. A promising approach in research analysis structural functional brain connectomes, i.e., sNETs fNETs, respectively. We propose to use tensor representation (B-tensor) uni-modal multi-modal connectomes define a low-dimensional space via...

How can we decompose a data tensor if the indices are partially missing? Tensor decomposition is a fundamental tool to analyze the tensor data. Suppose, for example, we have a 3rd-order tensor X where each element Xijk takes 1 if user i posts word j at location k on Twitter. Standard tensor decomposition expects all the indices are observed. However, in some tweets, location k can be missing. I...