Related papers: Nil-clean companion matrices

We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…

We study spaces of reflectionless Jacobi matrices. The main theme is the following type of question: Given a reflectionless Jacobi matrix, is it possible to approximate it by other reflectionless and, typically, simpler Jacobi matrices of a…

We review recent developments towards models for neutrino masses and mixings.

We answer two questions posed 1998 in the book 'Arnolds problems'. First, over any field k there is a representative system for the similarity classes of nxn-matrices which is a finite disjoint union of affine subspaces. And second, for n>1…

We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple Z-graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered. In certain…

We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…

For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical…

The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…

We apply Nelson's technique of constructing Euclidean fields to the case of classical scalar fields on curved spaces. It is shown how to construct a transfer matrix and, for a class of metrics, the basic spectral properties of its generator…

The equation of state of a family of alternative linear chiral models in the mean field approximation is discussed. We investigate the analogy between some of these models with current models in the literature, and we show that it is…

We discuss the connections tying Laplacian matrices to abstract duality and planarity of graphs.

We consider a class of finite-dimensional algebras, the so-called "Staircase algebras" parametrized by Young diagrams. We develop a complete classification of representation types of these algebras and look into finite, tame (concealed) and…

We describe derivations of several important associative and Lie rings of infinite matrices over general rings of coefficients.

We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…

We revisit the matrix problems sparse null space and matrix sparsification, and show that they are equivalent. We then proceed to seek algorithms for these problems: We prove the hardness of approximation of these problems, and also give a…

We prove that every nonderogatory matrix $A$ over a field of positive odd characteristic $p,$ that is sum of a $p$-potent matrix and a nilpotent matrix, has a decomposition $A=E+V,$ such that $E^p=E,$ and $V^3=0.$

In this paper, we use elementary method to give a classification of the multiplicative maps on matrix algebra $M_{n}(\mF)$ over a field $\mF$ of characteristic $0$. All the multiplicative maps are classified into three classes: the trivial…

We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of…

We determine when a matrix is similar to a partial isometry, refining a result of Halmos--McLaughlin.

The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is…