Related papers: When a matrix condition implies the Mal'tsev prope…
This paper addresses various questions about pairs of similarity classes of matrices which contain commuting elements. In the case of matrices over finite fields, we show that the problem of determining such pairs reduces to a question…
In this paper, several versions of the Kolmogorov-Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight $W$ is in the known $A_p$ class, a characterization of totally…
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
We give conditions for when the tensor product of two positive maps between matrix algebras is a positive map. This happens when one map belongs to a symmetric mapping cone and the other to the dual cone. Necessary and sufficient conditions…
A theorem of Mandel allows to determine the covector set of an oriented matroid from its set of topes by using the composition condition. We provide a generalization of that result, stating that the covector set of a conditional oriented…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…
While every matrix algebra over a field $K$ can be realized as a Leavitt path algebra, this is not the case for every graded matrix algebra over a graded field. We provide a complete description of graded matrix algebras over a field,…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely…
For a class of symmetric random matrices whose entries are martingale differences adapted to an increasing filtration, we prove that under a Lindeberg-like condition, the empirical spectral distribution behaves asymptotically similarly to a…
Many economic theory models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. We provide a principled framework for scaling results from such models by removing these finiteness…
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…
In this paper we study the low rank matrix completion problem using tools from Schur complement. We give a sufficient and necessary condition such that the completed matrix is globally unique with given data. We assume the observed entries…
Let $B \subseteq A$ be an extension of finite dimensional algebras. We provide a sufficient condition for the existence of triangle equivalences of singularity categories (resp. Gorenstein defect categories) between $A$ and $B$. This result…
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
The notion of Igusa-Todorov classes is introduced in connection with the finitistic dimension conjecture. As application we consider conditions on special ideals which imply the Igusa-Todorov and other finiteness conditions on modules…
We relate the theory of purity of a locally finitely presented category with products to the study of exact structures on the full subcategory of finitely presented objects. Properties in the context of purity are translated to properties…
A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…
Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…
In this work, we extend the concept of the double of an ideal defined in \cite{G2}, to the context of modules. We also obtain the genericity of the infinitesimal Lipschitz condition A for an enlarged class of analytic spaces.