Related papers: Computing Tensor Generalized bilateral inverses
Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e.…
Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…
There has been proposed a new method of the constructing of the basic functions for spaces of tensor representations of the Lie groups with the help of the generalized Casimir operator. In the definition of the operator there were used the…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To…
We are upgrading the Python-version of RTNI, which symbolically integrates tensor networks over the Haar-distributed unitary matrices. Now, PyRTNI2 can treat the Haar-distributed orthogonal matrices and the real and complex normal Gaussian…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
We consider an algebra of even-order square tensors and introduce a stretching map which allows us to represent tensors as matrices. The stretching map could be understood as a generalized matricization. It conserves algebraic properties of…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
We present an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical…
Iterated commutators of multilinear Calderon-Zygmund operators and pointwise multiplication with functions in $BMO$ are studied in products of Lebesgue spaces. Both strong type and weak end-point estimates are obtained, including weighted…
Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…
It is well known that a square complex matrix is called EP if it commutes with its Moore-Penrose inverse. In this paper, new classes of matrices which extend this concept are characterized. For that, we consider commutative equalities given…
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
Let V be the representation of the quantised enveloping algebra of a general linear group which is the q-analogue of the vector representation. In this paper we construct a basis of the representations obtained by tensoring copies of V and…
The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to…