Related papers: Generalized matrix functions on a linear sum of pe…
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…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
We prove inequalities on non-integer powers of products of generalized matrices functions on the sum of positive semi-definite matrices. For example, for any real number $r \in \{1\} \cup [2, \infty)$, positive semi-definite matrices $A_i,\…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
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.
A generalized matrix function $d_\chi^G : M_n(\mathbb{C}) \rightarrow \mathbb{C}$ is a function constructed by a subgroup $G$ of $S_n$ and a complex valued function $\chi$ of $G$. The main purpose of this paper is to find a necessary and…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
We show that the permanent of a matrix can be written as the expectation value of a function of random variables each with zero mean and unit variance. This result is used to show that Glynn's theorem and a simplified MacMahon theorem…
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 paper addresses the calculation of correlation functions of permanental polynomials of matrices with random entries. By exploiting a convenient contour integral representation of the matrix permanent some explicit results are provided…
In this paper, the exact values of the structured singular values of some generalized stochastic complex matrices is explicit in term of the constant row (column) sum.
The main purpose of this paper of the paper is an explicite construction of generalized Gaussian process with function $t_b(V)=b^{H(V)}$, where $H(V)=n-h(V)$, $h(V)$ is the number of singletons in a pair-partition $V \in \st{P}_2(2n)$. This…
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…
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…
This paper investigates the generalized beta-logarithmic matrix function (GBLMF),which combines the extended beta matrix function and the logarithmic mean. The study establishes essential properties of this function, including functional…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…
We introduce a generalized Grover matrix of a graph and present an explicit formula for its characteristic polynomial. As a corollary, we give the spectra for the generalized Grover matrix of a regular graph. Next, we define a zeta function…
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for the Macdonald functions.