Related papers: Double B-tensor and quasi-double B-tensor

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

We classify the algebraic curvature tensors which are both Osserman and complex Osserman in all but a finite number of exceptional dimensions.Information concerning the possible eigenvalue structures, which is provided by methods of…

A generalization of Ricci-like solitons with torse-forming potential, which is a constant multiple of the Reeb vector field, is studied. The conditions under which these solitons are equivalent to almost Einstein-like metrics are given.…

We study almost squareness and the strong diameter two property in the setting of projective (symmetric) tensor product. We prove that almost squareness is preserved by taking projective tensor product, providing non-trivial examples of ASQ…

Hankel tensors arise from signal processing and some other applications. SOS (sum-of-squares) tensors are positive semi-definite symmetric tensors, but not vice versa. The problem for determining an even order symmetric tensor is an SOS…

Two-grid theory plays a fundamental role in the design and analysis of multigrid methods. This paper is devoted to a new convergence analysis of two-grid methods for singular and symmetric positive semidefinite systems. Specifically, we…

We introduce $\hat{H}$-eigenvalue for $2m$-th order $n$-dimensional complex tensors. Then we determine several checkable inclusion sets for $\hat{H}$-eigenvalues and derive some criterions for the Hermitian positive definiteness…

By a tensor we mean a multidimensional array (matrix) or hypermatrix over a number field. This article aims to set an account of the studies on the permanent functions of tensors. We formulate the definitions of 1-permanent, 2-permanent,…

Describing the gravitational energy and momentum, the Bel-Robinson tensor is the best tensor. However, the classical pseudotensors can also manage the the same job. As Deser mentioned in 1999, a certain linear combination between Einstein…

In this article, we mainly give the strictly copositive conditions of a special class of third order three dimensional symmetric tensors. More specifically, by means of the polynomial decomposition method, the analytic sufficient and…

We propose and study the properties of a new potential demanded by the self-consistency of the duality scheme in electromagnetic-like field theories of totally anti-symmetric tensors in diverse dimensions. Physical implications of this new…

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a…

The tensor complementarity problem is a specially structured nonlinear complementarity problem, then it has its particular and nice properties other than ones of the classical nonlinear complementarity problem. In this paper, it is proved…

We construct the tensor hierarchies of generic, bosonic, 5- and 6-dimensional field theories. The construction of the tensor hierarchy starts with the introduction of two tensors: the embedding tensor which tells us which vector is used for…

A generalization of duality transformations for arbitrary Lorentz tensors is presented, and a systematic scheme for constructing the dual descriptions is developed. The method, a purely Lagrangian approach, is based on a first order parent…

Persistent tensors, introduced in [Quantum 8 (2024), 1238], and inspired by quantum information theory, form a recursively defined class of tensors that remain stable under the substitution method and thereby yield nontrivial lower bounds…

We introduce a total order and the absolute value function for dual numbers. The absolute value function of dual numbers are with dual number values, and have properties similar to the properties of the absolute value function of real…

Rank-2 and rank-3 tensors are almost all identifiable with only few exceptions. We classify them all together with the dimensions and the structures of all the sets evincing the rank.

We consider Bel-Robinson-like higher derivative conserved two-index tensors $H_\mn$ in simple matter models, following a recently suggested Maxwell field version. In flat space, we show that they are essentially equivalent to the true…

In this paper, we study the approximate orthogonal diagonalization problem of third order symmetric tensors. We define several classes of approximately diagonal tensors, including the ones corresponding to the stationary points of this…