Related papers: Generalized matrix coefficients of Unitary Represe…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary…
In this paper, we describe the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…
We introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showing that in the null case of uncorrelated variables, the…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
An introductory to generalized parton distributions is given which emphasizes their spectral property and its uses as well as the equivalence of various GPD representations. Furthermore, the status of the theory and phenomenology of hard…
Matrix multivariate Pearson type II-Riesz distribution is defined and some of its properties are studied. In particular, the associated matrix multivariate beta distribution type I is derived. Also the singular values and eigenvalues…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
In this paper, closed formulas for the eigenvectors of a particular class of matrices generated by generalized permutation matrices, named generalized circulant matrices, are presented.
Generalized Pascal matrix whose elements are generalized binomial coefficients is included in the group of generalized Riordan arrays. There is a special set of generalized Riordan arrays defined by parameter $q$. If $q=0$, they are…
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold…
By polynomial (or extended binomial) coefficients, we mean the coefficients in the expansion of integral powers, positive and negative, of the polynomial $1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish several…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
In this paper, we give a practical method to compute the Jacobian matrices of generalized Chebyshev polynomials associated to arbitrary semisimple Lie algebras. The entries of each Jacobian matrix can be expressed as a linear combination of…
The link between the nucleon generalized parton distributions and the non-diagonal one-body density matrix in momentum space is studied. Attention is focussed on the region where quark generalized parton distributions (GPD's) describe…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
The corepresentation theory of continuous groups is presented without the assumption that the subgroup $G$ of the group with antilinear operations is unitary. The formulas of the corepresentation theory with unitary groups $G$ can be…
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on…
A general description of the Vi\`ete coefficients of the gaussian period polynomials is given, in terms of certain symmetric representations of the subgroups and the corresponding quotient groups of the multiplicative group…
The most fundamental notion for Hilbert space frames is the sequence of frame coefficients for a vector x in the space. Yet, we know little about the distribution of these coefficient sequences. In this paper, we make the first detailed…