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Related papers: A Note on a Unitary Analog to Redheffer's Matrix

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A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…

Combinatorics · Mathematics 2014-11-20 Ron M. Adin , Yuval Roichman

The deep interconnection between linear algebra and graph theory allows one to interpret classical matrix invariants through combinatorial structures. To each square matrix A over a commutative ring K, one can associate a weighted directed…

Combinatorics · Mathematics 2025-11-11 Sudip Bera

We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.

Mathematical Physics · Physics 2022-05-06 Nicolas Babinet , Taro Kimura

In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers…

Combinatorics · Mathematics 2007-05-23 Sharon J. X. Hou , Jiang Zeng

Let P be the set of the sequence of polynomials of degree n. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help…

Number Theory · Mathematics 2022-02-24 Dae san Kim , taekyun Kim

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…

Number Theory · Mathematics 2018-05-16 Yilmaz Simsek

We study monic univariate polynomials whose coefficients are analytic functions of a real variable and whose roots lie in a specified analytic curve. These include characteristic polynomials of unitary and hermitian matrices whose entries…

Algebraic Geometry · Mathematics 2012-03-01 Wayne Lawton

This note presents several conditions to characterize real matrix similarity between a Hurwitz matrix (and then more generally, a real square matrix) and a diagonal dominant matrix.

Optimization and Control · Mathematics 2023-02-24 Zhiyong Sun , Brian D. O. Anderson , Wei Chen

We give new definitions for the determinant over commutative ring $K$, noncommutative ring $\mathbf{K}$, noncommutative ring $\mathcal{K}$ with associative powers, over noncommutative nonassociative ring $\mathfrak{K}$, and study their…

Combinatorics · Mathematics 2012-01-04 Georgy Egorychev

Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8.

Number Theory · Mathematics 2008-07-03 Roland Bacher

It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…

Dynamical Systems · Mathematics 2025-03-17 Ziyad AlSharawi , Jose S. Cánovas , Sadok Kallel

The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of…

Number Theory · Mathematics 2025-01-13 Taekyun Kim , Dae san Kim

A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of…

Probability · Mathematics 2022-05-23 Patryk Pagacz , Michał Wojtylak

We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a function to compute its matrix-vector product. The methods apply to…

Symbolic Computation · Computer Science 2009-05-18 Jean-Guillaume Dumas , Clément Pernet , B. David Saunders

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum…

Representation Theory · Mathematics 2010-08-10 Claudio Gorodski

We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well…

Probability · Mathematics 2015-10-05 Christian Webb

This note presents some equalities in law for $Z_N:=\det(\Id-G)$, where $G$ is an element of a subgroup of the set of unitary matrices of size $N$, endowed with its unique probability Haar measure. Indeed, under some general conditions,…

Probability · Mathematics 2007-06-22 Paul Bourgade , Ashkan Nikeghbali , Alain Rouault

A square matrix is $k$-Toeplitz if its diagonals are periodic sequences of period $k$. We find universal formulas for the determinant, the characteristic polynomial, some eigenvectors, and the entries of the inverse of any tridiagonal…

Rings and Algebras · Mathematics 2023-01-04 Jose Brox , Helena Albuquerque

We generalize a previous inequality related to a sharp version of the Littlewood conjecture on the minimal $L_1$-norm of $N$-term exponential sums $f$ on the unit circle. The new result concerns replacing the expression $\log(1+t|f|^2)$…

Classical Analysis and ODEs · Mathematics 2011-01-11 Ivo Klemes

An $F$-algebra $A$ with unit $1$ is said to be a locally matrix algebra if an arbitrary finite collection of elements $a_1,$ $\ldots,$ $a_s $ from $ A$ lies in a subalgebra $B$ with $1$ of the algebra $A$, that is isomorphic to a matrix…

Rings and Algebras · Mathematics 2019-07-29 Oksana Bezushchak , Bogdana Oliynyk
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