相关论文: Three families of matrices

The main result of the paper is a classification of singularities of complex skew-symmetric matrix families of even size which are simple under a natural equivalence relation. The classification is obtained by appropriate suspensions of…

Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…

Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory.…

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…

Matrices over the dual numbers are considered. We propose an approach to classify these matrices up to similarity. Some preliminary results on the realization of this approach are obtained. In particular, we produce explicitly canonical…

In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…

In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive…

A new family of maximal curves over a finite field is presented and some of their properties are investigated.

In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…

The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…

The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…

In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…

In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

The problem we are considering came up in connection with the classification of singularities in positive characteristic. Then it is important that certain invariants like the determinacy can be bounded simultaneously in families of formal…

An operator matrix $H$ associated with a lattice system describing three particles in interactions, without conservation of the number of particles, is considered. The structure of the essential spectrum of $H$ is described by the spectra…

In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

Using the language of finite element exterior calculus, we define two families of $H^1$-conforming finite element spaces over pyramids with a parallelogram base. The first family has matching polynomial traces with tensor product elements…

We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…