Related papers: Tensor Transpose and Its Properties
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…
This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based…
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square…
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…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…
In this article, we define a matrix variate asymmetric Laplace distribution. We prove some properties of the matrix variate asymmetric Laplace distribution. We prove the relationship between the matrix variate asymmetric Laplace…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
Transverse-momentum spectra in hard processes are typically described either in terms of intrinsic transverse momentum of partons, or in terms of perturbative radiation. The relation between these descriptions is discussed for the example…
The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us…
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
We define super-energy tensors for arbitrary physical fields, including the gravitational, electromagnetic and massless scalar fields. We also define super-super-energy tensors, and so on. All these tensors satisfy the so-called "Dominant…
We define two new constants associated with real eigenvalues of a P-tensor. With the help of these two constants, in the case of P-tensors, we establish upper bounds of two important quantities, whose positivity is a necessary and…
In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…