Related papers: Nil-clean companion matrices
The literature about strongly clean matrices over commutative rings is quite extensive. The sharpest results are about matrices over commutative local rings, for example those by Borooah, Diesl and Dorsey. The purpose of this note is to…
Frobenius companion matrices arise when we write an $n$-th order linear ordinary differential equation as a system of first order differential equations. These matrices and their transpose have very nice properties. By using the powers of…
We classify $G$-solid rational surfaces over the field of complex numbers.
We extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a…
We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.
Power nonnegative matrices are defined as complex matrices having at least one nonnegative integer power. We exploit the possibility of deriving a Perron Frobenius-like theory for these matrices, obtaining three main results and drawing…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
Following the procedures by which O(N)-invariant real vector models and their large-N behavior have previously been solved, we extend similar techniques to the study of real symmetric N x N-matrix models with O(N)-invariant interactions.…
In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…
We give a presentation of abelian class field theory.
We study the relation between the existence of null conformal Killing vector fields and existence of compatible complex and para-hypercomplex structures on a pseudo-Riemannian manifold with metric of signature (2,2). We establish first the…
The paper continues nlin.SI/0212019 by giving three more examples of using cyclic bases of zero-curvature representations in studies of relation between strong Lax pairs and recursion operators.
Almost-commuting matrices with respect to the normalized Hilbert-Schmidt norm are considered. Normal almost commuting matrices are proved to be near commuting.
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries
We prove coherence of relatively quasi-free algebras over noetherian rings. Chase criterion for coherence is used.
For certain rings $\mathcal{R}$, we construct explicit matrices representing nonzero classes in the algebraic $K$ theory group $NK_{1}(\mathcal{R})$.