Related papers: Inertia tensor and cross product In n-dimensions s…

We explain how, in the context of a semi-abelian category, the concept of an internal crossed square may be used to set up an intrinsic approach to the Brown-Loday non-abelian tensor product.

In this manuscript, we present a common tensor framework which can be used to generalize one-dimensional numerical tasks to arbitrary dimension $d$ by means of tensor product formulas. This is useful, for example, in the context of…

Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…

This paper extends the univariate Theory of Connections, introduced in (Mortari,2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface,…

We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal spaces in the general case, classify all the monomial spaces in the case of…

The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…

We consider the set of pairs of orthogonal vectors in Hilbert space, which is also called the cross because it is the union of the horizontal and vertical axes in the Euclidean plane when the underlying space is the real line. Crosses,…

We define and study a certain relative tensor product of subfactors over a modular tensor category. This gives a relative tensor product of two completely rational heterotic full local conformal nets with trivial superselection structures…

In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications…

We classify weakly Einstein algebraic curvature tensors in an oriented Euclidean 4-space, defined by requiring that the three-index contraction of the curvature tensor against itself be a multiple of the inner product. This algebraic…

The question of whether a split tensor product of quaternion algebras with involution over a field of characteristic two can be expressed as a tensor product of split quaternion algebras with involution, is shown to have an affirmative…

We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a…

In this work we provide a definition of the constraint tensor of a null hypersurface data which is completely explicit in the extrinsic geometry of the hypersurface. The definition is fully covariant and applies for any topology of the…

It was proposed that the tensor product structure of the Hilbert space is uniquely determined by the Hamiltonian's spectrum, for most finite-dimensional cases satisfying certain conditions. I show that any such method would lead to…

In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…

We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of $0$-symmetric convex bodies in Euclidean spaces. We prove that there is a bijection between tensor products of…

Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner…

We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries…

Applications of the theory and computations of boolean matrices are of fundamental importance to study a variety of discrete structural models. But the increasing ability of data collection systems to store huge volumes of multidimensional…

Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate $C^\infty$ cutoff functions. These tools are further employed to the development…