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The rotation of multi-dimensional arrays, or tensors, is a fundamental operation in computer science with applications ranging from data processing to scientific computing. While various methods exist, achieving this rotation in-place…
In the past five years, there has been considerable research on the collider phenomenology of TeV-scale extra compact dimensions which are universal - i.e. accessible to all the Standard Model fields. We consider in detail a fundamental…
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…
Using the tensor product variety introduced by Malkin and Nakajima, the complete structure of the tensor product of a finite number of integrable highest weight modules of U_q(sl_2) is recovered. In particular, the elementary basis,…
The representation theory of tensor functions is essential to constitutive modeling of materials including both mechanical and physical behaviors. Generally, material symmetry is incorporated in the tensor functions through a structural or…
In this paper we introduce techniques to gauge the torsion of the tensor product $A\otimes_RB$ of two finitely generated modules over a Noetherian ring $R$. The outlook is very different from the study of the rigidity of Tor carried out in…
The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Tensor product operators on finite dimensional Hilbert spaces are studied. The focus is on bilinear tensor product operators. A tensor product operator on a pair of Hilbert spaces is a maximally general bilinear operator into a target…
In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and…
We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
In this paper, the $mn$-dimensional space of tensor-product polynomials of two variables, of degree at most $(m-1)+(n-1)$, is considered. A theory of two-variate polynomials is developed by establishing the algebra and basic algebraic…
A unified field theory for the description of matter in a curved space is discussed. The description is based on a standard Lagrangianian formalism in a pseudo-Euclidian 4D continuum using a 3-index tensor as independent variables. The…
This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable…
By means of the rotational transformations of octonion coordinate systems, the paper aims to explore the physical properties of conserved quantities relevant to the vectorial magnitudes within the material media, revealing the simultaneity…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…
We characterise the embedding of the spatial product of two Arveson systems into their tensor product using the random set technique. An important implication is that the spatial tensor product does not depend on the choice of the reference…
We show that each irreducible tensor representation of weight 2 of the rotation group of three-dimensional space in the space of rank 3 covariant tensors gives rise to an associative algebra with unity. We find the algebraic relations that…