Ordering D-classes and computing Schein rank is hard.
Perimeter preservers of nonnegative integer matrices
We investigate the perimeter of nonnegative integer matrices. We also characterize the linear operators which preserve the rank and perimeter of nonnegative integer matrices. That is, a linear operator preserves the rank and perimeter of rank- matrices if and only if it has the form , or with appropriate permutation matrices and and positive integer matrix , where denotes Hadamard product.
Positive factors of Wythoff matrices.
Products of idempotent matrices over Hermite domains.
Propriétés des matrices «bien localisées» près de leur diagonale et quelques applications
Relationship of certain rings of infinite matrices over integers
Sia l'insieme degli interi non negativi e l'anello degli interi. Sia l'anello delle matrici su che hanno solo un numero finito di cifre non nulle in ogni linea ed in ogni colonna. Sia il sottoanello generato da e , dove (rispettivamente ) è ottenuto dalla matrice identità muovendo gli 1 una posizione a destra (rispettivamente in giù). Sia pure il sottoanello di generato da e . Infine sia il sottoanello delle matrici di che hanno solo un numero finito di cifre non nulle....
Representations of semigroups of idempotents
Semigroups of finite matrices.
Some constructions related to Rees matrix rings.
Some decision problems on integer matrices
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension , questions 1) and 3) are undecidable. For dimension , they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...
Some decision problems on integer matrices
Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...
Some Examples of Rigid Representations
*Research partially supported by INTAS grant 97-1644.Consider the Deligne-Simpson problem: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) (resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp. A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann’s sphere. We give new examples...
Some observations on the Lah and Laguerre transforms of integer sequences.
Sous-groupes distingues du groupe unitaire et du groupe général linéaire d'un espace de Hilbert quaternionien.
Sous-groupes distingués du groupe unitaire et du groupe général linéaire d'un espace de Hilbert
Spaces of constant rank matrices over .
Stable subnorms on finite-dimensional power-associative algebras.
The algebra of the subspace semigroup of
The semigroup of subspaces of the algebra of 2 × 2 matrices over a finite field is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.
The equations of conjugacy classes of nilpotent matrices.
The Rational Invariants of the Tame Quivers.