Related papers: Stretching maps for tensors
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
We consider a class of maps from integral Hankel operators to Hankel matrices, which we call restriction maps. In the simplest case, such a map is simply a restriction of the integral kernel onto integers. More generally, it is given by an…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth…
The main purpose of this paper is to introduce the random tensor with normal distribution, which promotes the matrix normal distribution to a higher order case. Some basic knowledge on tensors are introduced before we focus on the random…
We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…
Tensors are multidimensional analogs of matrices. In this paper, based on degree-theoretic ideas, we study homogeneous nonlinear complementarity problems induced by tensors. By specializing this to $Z$-tensors (which are tensors with…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introduced. Some algebraic and…
We introduce a generalization of representations of quivers that contains also representations of posets, vectorspace problems and other matrix problems. Many examples, some of which are given in the paper, show that the language of marked…
Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…
We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
We introduce and study the crossing map, a closed linear map acting on operators on the tensor square of a given Hilbert space that is inspired by the crossing property of quantum field theory. This map turns out to be closely connected to…
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…