Related papers: Generalized matrix coefficients of Unitary Represe…

We generalize the concept of Pascal matrices to matrices associated with sets of points by considering multidimensional binomial coefficients as entries. We study their properties and prove that the infinite matrix associated with the set…

A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…

We start by presenting a generalization of a discrete wave equation that is particularly satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are…

We calculate Gaussian averages of arbitrary exponentials of the matrix variable $X$ with the help of superintegrability, which provides explicit expressions for Schur averages. As in the simpler cases the answer is expressed in terms of…

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…

It was observed in \cite{Al2} that the expectation of a squared scalar product of two random independent unit vectors that are uniformly distributed on the unit sphere in $\mathbb{R}^n $ is equal to $1/n$. It is shown below that this is a…

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…

We develop representation theory approach to the study of special functions associated with toric varieties. In particular we show that the corresponding special functions are given by matrix elements of certain non-reductive Lie algebras

We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$…

Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups ($GL_n$). The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for…

In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…

A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…

Let $k$ be a local field of characteristic 0, and let $G$ be a connected semisimple almost $k$-algebraic group. Suppose rank$_kG\geq 1$ and $\rho$ is an excellent representation of $G$ on a finite dimensional $k$-vector space $V$. We…

Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…

We present a numerical implementation of generalized unitarity. We will show that we are able to obtain the box coefficients of any 1 loop gluonic amplitude, for an arbitrary helicity configuration and for any number of external particles.

Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…

We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…

An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…

In this paper, we introduce a new concept of generalized matrix rings and build up the general theory of radicals for g.m.rings. Meantime, we obtain $$\bar{r}_b(A)=g.m.r_b(A)=\sum\{r_b(A_{ij})\mid i, j\in I\}=r_b(A)$$

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…