Related papers: On the computation of tensor functions under tenso…

These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…

The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…

This paper discusses the computation of real Z-eigenvalues and H-eigenvalues of nonsymmetric tensors. A general nonsymmetric tensor has finitely many Z-eigenvalues, while there may be infinitely many ones for special tensors. In the…

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…

In general, matrix or tensor-valued functions are approximated using the method developed for vector-valued functions by transforming the matrix-valued function into vector form. This paper proposes a tensor-based interpolation method to…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra…

Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…

Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

We suggest a new, alternative algebraic method for computation of geometrical quantities by means of the embedding of local loops into Lie groups.

Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…

In a paper published in 1981, Sch\"onhage showed that large total matrix multiplications can be reduced to powers of partial matrix multiplication tensors, which correspond to the bilinear computation task of multiplying matrices with some…

In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the…

We show how the theory of $\mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such…

One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…

We provide a computer algebra package called Random Tensor Network Integrator (RTNI). It allows to compute averages of tensor networks containing multiple Haar-distributed random unitary matrices and deterministic symbolic tensors. Such…

Using Hilbert's criterion, we consider the stress-energy tensor associated to the bienergy functional. We show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four. First, we use this tensor to…

We present different methods for symbolic computer algebra computations in higher dimensional (\ge9) Clifford algebras using the \Clifford\ and \Bigebra\ packages for \Maple(R). This is achieved using graded tensor decompositions,…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…