AbstractWe consider the group SLnF of all n × n matrices with determinant 1 over a field. Let res A denote rank (A - I) for any A in GLnF. A matrix A ∈ GLnF is called a dilatation if A is similar to a matrix In−1 ⊕ a (a ≠ 1). We prove that if |F| > 4, then every matrix A in SLnF is the product of at most [res A/2] + 1 commutators of dilatations for n ≥ 2
AbstractProblem: Given operators Aj ⩾ O on Hilbert space H, with ΣAj = 1, to find commuting projecto...
Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F...
AbstractThe well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determi...
AbstractWe consider the group SLnF of all n × n matrices with determinant 1 over a field. Let res A ...
AbstractWe consider the group SLnF of all n×n matrices with determinant 1 over a field F. We prove t...
AbstractLet F be a division ring and AϵGLn(F). We determine the smallest integer k such that A admit...
AbstractLet R be a commutative local ring, and M the maximal ideal of R. We prove that if |R/M|>3, t...
AbstractGiven a nontrivial conjugacy class Ω of GL(V) which is contained in SL(V), we want to find a...
AbstractWe consider the group GLnA of all invertible n by n matrices over a ring A satisfying the fi...
AbstractWe consider the group SLnF of all n by n matrices with determinant 1 over a field. Let res A...
AbstractKovacs (J. Combin. Theory, Ser. A 45 (1987), 290–299) has derived an expression for the numb...
AbstractEvery square matrix over a field, with determinant ±1, is the product of not more than four ...
AbstractThis note gives explicit factorizations of a 2 × 2 operator matrix as a product of an upper ...
AbstractAn n by n matrix M over a (commutative) field F is said to be central if M − I has rank 1. W...
AbstractGiven any norm u(·) on the space of linear transformations (matrices) over a finite-dimensio...
AbstractProblem: Given operators Aj ⩾ O on Hilbert space H, with ΣAj = 1, to find commuting projecto...
Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F...
AbstractThe well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determi...
AbstractWe consider the group SLnF of all n × n matrices with determinant 1 over a field. Let res A ...
AbstractWe consider the group SLnF of all n×n matrices with determinant 1 over a field F. We prove t...
AbstractLet F be a division ring and AϵGLn(F). We determine the smallest integer k such that A admit...
AbstractLet R be a commutative local ring, and M the maximal ideal of R. We prove that if |R/M|>3, t...
AbstractGiven a nontrivial conjugacy class Ω of GL(V) which is contained in SL(V), we want to find a...
AbstractWe consider the group GLnA of all invertible n by n matrices over a ring A satisfying the fi...
AbstractWe consider the group SLnF of all n by n matrices with determinant 1 over a field. Let res A...
AbstractKovacs (J. Combin. Theory, Ser. A 45 (1987), 290–299) has derived an expression for the numb...
AbstractEvery square matrix over a field, with determinant ±1, is the product of not more than four ...
AbstractThis note gives explicit factorizations of a 2 × 2 operator matrix as a product of an upper ...
AbstractAn n by n matrix M over a (commutative) field F is said to be central if M − I has rank 1. W...
AbstractGiven any norm u(·) on the space of linear transformations (matrices) over a finite-dimensio...
AbstractProblem: Given operators Aj ⩾ O on Hilbert space H, with ΣAj = 1, to find commuting projecto...
Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F...
AbstractThe well-known determinantal cinjecture of de Oliveira and Marcus (OMC) confines the determi...
DOI
Add to ORKG