Related papers: Generalized matrix coefficients of Unitary Represe…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
The determinant of the Gaussian unitary ensemble matrix is show to be distributed as a product of independent chi random variables with parameters $1,3,3,5,5,\dots.$
We study matrix coefficients of the unitary (and also the completely bounded) representations of SL(2;R) and its universal covering group. We describe the asymptotic distribution of column vectors in terms of Whittaker functions, exhibiting…
We provide a new and simple characterization of the multivariate generalized Laplace distribution. In particular, this result implies that the product of a Gaussian matrix with independent and identically distributed columns by an…
We formalize the notion of matrix coefficients for distributional vectors in a representation of a real reductive group, which consist of generalized functions on the group. As an application, we state and prove a Gelfand-Kazhdan criterion…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.
We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term ${}_1F_1$ in the non-central uni-variate Student's $t$. Some extensions of matrix-variate distributions…
Supposing Kotz-Riesz type I and II distributions and their corresponding independent univariate Riesz distributions the associated generalised matrix multivariate T distributions, termed matrix multivariate T-Riesz distributions are…
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 study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…
We define generalized bivariate polynomials, from which upon specification of initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series…
The generalized vector is defined on an $n$ dimensional manifold. Interior product, Lie derivative acting on generalized $p$-forms, $-1\le p\le n$ are introduced. Generalized commutator of two generalized vectors are defined. Adding a…