Related papers: Tensor Commutation Matrices and Some Generalizatio…
In this text we review a few structural properties of matrix models that should at least partly generalize to random tensor models. We review some aspects of the loop equations for matrix models and their algebraic counterpart for tensor…
We propose a novel matrix regularization for tensor fields. In this regularization, tensor fields are described as rectangular matrices and both area-preserving diffeomorphisms and local rotations of the orthonormal frame are realized as…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
We study various conditions under which a unitary in an ultraproduct of matrices is conjugated to an ultraproduct of permutations.
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…
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the…
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…
Compact general formulae for the energy, momentum and angular momentum radiated by confined systems of charges and currents are presented in terms of their multipole Cartesian tensors. Besides the usual electric and magnetic multipoles, a…
Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
This paper introduces notions of the Drazin and the core-EP inverses on tensors via M-product. We propose a few properties of the Drazin and core-EP inverses of tensors, as well as effective tensor-based algorithms for calculating these…
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…
Let $\mathcal{A}$ be an order $t$ dimension $m\times n\times \cdots \times n$ tensor over complex field. In this paper, we study some {generalized inverses} of $\mathcal{A}$, the {$k$-T-idempotent tensors} and the idempotent tensors based…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard…
This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…
A generalized exponential matrix based on the construction of kernel operators for generalized summability is defined and analyzing its main properties, generalizing the classical exponential matrix and fractional exponential matrix. This…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…