Related papers: On stable range one matrices
We prove that every infinite sequence of skew-symmetric or symmetric matrices M_1, M_2, ... over a fixed finite field must have a pair M_i, M_j (i<j) such that M_i is isomorphic to a principal submatrix of the Schur complement of a…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
This study explores in-depth the structure and properties of the so-called {\it strongly $\Delta$-clean rings}, that is a novel class of rings in which each ring element decomposes into a sum of a commuting idempotent and an element from…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
We give an easy proof to show that every complex normal Toeplitz matrix is classified as either of type I or of type II. Instead of difference equations on elements in the matrix used in past studies, polynomial equations with coefficients…
We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to 2 legged spin ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by the…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
A commutative ring $R$ is projective free provided that every finitely generated $R$-module is free. An element in a ring is strongly clean provided that it is the sum of an idempotent and a unit that commutates. Let $R$ be a…
We propose matrix commutator based stability characterization for discrete-time switched linear systems under restricted switching. Given an admissible minimum dwell time, we identify sufficient conditions on subsystems such that a switched…
A noncommutative polynomial is stable if it is nonsingular on all tuples of matrices whose imaginary parts are positive definite. In this paper a characterization of stable polynomials is given in terms of strongly stable linear matrix…
We consider unimodular matrices $M$ such that neither $M$ nor $M^{-1}$ contain zero entries. Matrices typically exhibit a trade-off: small $M$ imply large $M^{-1}$. We investigate rare cases where both remain small, classify these matrices…
Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by…
We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix…
We generalize the 1/3-2/3 conjecture from partially ordered sets to antimatroids: we conjecture that any antimatroid has a pair of elements x,y such that x has probability between 1/3 and 2/3 of appearing earlier than y in a uniformly…
We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give some applications of such decompositions. Specifically, we…
The structure of the set of positivity-preserving maps between matrix algebras is notoriously difficult to describe. The notable exceptions are the results by St{\o}rmer and Woronowicz from 1960s and 1970s settling the low dimensional…
Let $A$ be a $\sigma$-unital finite simple $C^*$-algebra which has strict comparison property. We show that if the canonical map $\Gamma$ from the Cuntz semigroup to certain lower semi-continuous affine functions is surjective, then $A$ has…
We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…
We present a relation between stable rank one and real rank zero via the method of tracial oscillation. Let $A$ be a simple separable $C^*$-algebra of stable rank one. We show that $A$ has tracial approximate oscillation zero and, as a…