Related papers: Generalizations of Enestrom-Kakeya Type Theorems f…

Kasteleyn counted the number of domino tilings of a rectangle by considering a mutation of the adjacency matrix: a Kasteleyn matrix K. In this paper we present a generalization of Kasteleyn matrices and a combinatorial interpretation for…

This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…

We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero-Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials…

In this paper we bring to light an unprecedented property of the eigenvalues of a matrix A with the eigenvalues and eigenvectors of a submatrix of A. This property can be used, through the technique developed here, to determine some of…

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…

Let $R=K[x_{1},x_{2},\cdots, x_{m}]$ where $K$ is a field. In this paper, we give some properties of $n$-matrix factorizations of polynomials in $R$. We also derive some results giving some lower bounds on the number of $n$-matrix factors…

Using the Okounkov-Maulik stable map, we identify the equivariant cohomology of instanton moduli spaces with the space of polynomials on an infinite number of variables. We define the generalized Jack polynomials as the polynomials…

We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…

We give a common matroidal generalisation of `A Cantor-Bernstein theorem for paths in graphs' by Diestel and Thomassen and `A Cantor-Bernstein-type theorem for spanning trees in infinite graphs' by ourselves.

Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…

We prove a universal limit theorem for the halting time, or iteration count, of the power/inverse power methods and the QR eigenvalue algorithm. Specifically, we analyze the required number of iterations to compute extreme eigenvalues of…

Let (K, v) be a henselian valued field of arbitrary rank. In this paper, we give an irreducibility criterion for multivariate polynomials over K using valuation theory.

We improve the Cauchy radius of both scalar and matrix polynomials, which is an upper bound on the moduli of the zeros and eigenvalues, respectively, by using appropriate polynomial multipliers.

The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.

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.

We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices.

We derive bounds on the eigenvalues of saddle-point matrices with singular leading blocks. The technique of proof is based on augmentation. Our bounds depend on the principal angles between the ranges or kernels of the matrix blocks.…

We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. We first generalized a global-local theorem of Vaserstein. Then we proved these…

Symanzik polynomials are defined on Feynman graphs and they are used in quantum field theory to compute Feynman amplitudes. They also appear in mathematics from different perspectives. For example, recent results show that they allow to…