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Related papers: Some remarks on unilateral matrix equations

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The algebraic intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the algebraic intersection type…

Logic in Computer Science · Computer Science 2023-06-22 Andrej Dudenhefner , Moritz Martens , Jakob Rehof

We generalize classical triangular Schubert puzzles to puzzles with convex polygonal boundary. We give these puzzles a geometric Schubert calculus interpretation and derive novel combinatorial commutativity statements, using purely…

Combinatorics · Mathematics 2024-06-13 Portia Anderson

In this short note we make a few remarks on a class of generalized incidence matrices whose matroids do not depend on the orientation of the underlying graph and natural commutative algebras associated to such matrices.

Combinatorics · Mathematics 2020-05-14 Boris Shapiro , Arkady Vaintrob

Some inverse problems for semi-infinite periodic generalized Jacobi matrices are considered. In particular, a generalization of the Abel criterion is presented. The approach is based on the fact that the solvability of the Pell-Abel…

Classical Analysis and ODEs · Mathematics 2011-06-06 Maxim Derevyagin

Matrix integrals used in random matrix theory for the study of eigenvalues of matrix ensembles have been shown to provide $ \tau $-functions for several hierarchies of integrable equations. In this paper, we construct the matrix integral…

Exactly Solvable and Integrable Systems · Physics 2019-11-22 Bo-Jian Shen , Guo-Fu Yu

A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Special values of the parameters are characterized by the…

q-alg · Mathematics 2014-05-27 C. Frønsdal

We study a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory. They are defined as "noncommutative endomorphisms" of a polynomial algebra. More explicitly…

Quantum Algebra · Mathematics 2009-01-05 A. Chervov , G. Falqui , V. Rubtsov

We suggest an hierarchy of all the results known so far about the connection of the asymptotics of combinatorial or representation theoretic problems with ``beta=2 ensembles'' arising in the random matrix theory. We show that all such…

Combinatorics · Mathematics 2007-05-23 Alexei Borodin , Grigori Olshanski

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

Functional Analysis · Mathematics 2014-02-26 Jean-Christophe Bourin , Eun-Young Lee

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…

Rings and Algebras · Mathematics 2013-03-21 Charles R. Johnson , Helena Šmigoc , Dian Yang

New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…

Numerical Analysis · Mathematics 2012-03-13 Joseph F. Grcar

Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…

Classical Analysis and ODEs · Mathematics 2021-02-09 Gennaro Infante

We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…

Rings and Algebras · Mathematics 2019-07-31 Nam van Tran , Imme van den Berg

In this paper, we establish an analogue of the Fundamental Theorem of Algebra for polynomial matrix equations, where both the coefficient matrices and the unknown matrix are $Q$-circulant matrices. This result generalizes Abramov's result…

Rings and Algebras · Mathematics 2026-01-21 Hongjian Li

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory results for linearizations need to be related back to matrix polynomials. In this paper we…

Numerical Analysis · Mathematics 2020-08-06 Andrii Dmytryshyn

We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…

Mathematical Physics · Physics 2016-11-30 Marc Briant

For any unitary matrix there exists a ZXZ decomposition, according to a theorem by Idel and Wolf. For any even-dimensional unitary matrix there exists a block-ZXZ decomposition, according to a theorem by F\"uhr and Rzeszotnik. We conjecture…

Quantum Physics · Physics 2021-12-02 Alexis De Vos , Martin Idel , Stijn De Baerdemacker

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…

Dynamical Systems · Mathematics 2013-10-03 António J. G. Bento , César M. Silva

We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…

Strongly Correlated Electrons · Physics 2026-03-20 Joseph M. Jones , M. W. Long

A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically…

Geometric Topology · Mathematics 2007-05-23 Ryan Budney
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