12 research outputs found
Two parametric quasi-cyclic codes as hyperinvariants subspaces
It is known the relationship between cyclic codes and
invariant subspaces. In this work we present a general-
ization considering âgeneralizedâ cyclic codes and hy-
perinvariant subspacesPostprint (published version
Cyclic codes as hyperinvariant subspaces
It is known the relationship between cyclic codes and
invariant subspaces. We present in this work some
codes which are obtained from invariant and hyperinvariant
subspaces of the linear maps having associated
matrices, in the standard basis, of a special form. xxxPostprint (published version
Switched linear systems. Geometric approach
We consider equivalence relation between switched
linear systems and compute the dimension of equivalence
classes, after proving they can be obtained as the
orbits of the action of a Lie group on the differentiable
manifold of matrices defining the subsystems the system
consists of and deduce miniversal deformation
On the existence of a common eigenvector for all matrices in the commutant of a single matrix
The main purpose of this paper is to study common invariant subspaces of any matrix in the centralizer of a given matrix AâMn(F), where F denotes an algebraically closed field. In particular, we obtain a necessary and sufficient condition for the existence of a common eigenvector for all the matrices in this set.Peer ReviewedPostprint (published version
On the existence of a common eigenvector for all matrices in the commutant of a single matrix
The main purpose of this paper is to study common invariant subspaces of any matrix in the centralizer of a given matrix AâMn(F), where F denotes an algebraically closed field. In particular, we obtain a necessary and sufficient condition for the existence of a common eigenvector for all the matrices in this set.Peer Reviewe
Switched linear systems. Geometric approach
We consider equivalence relation between switched
linear systems and compute the dimension of equivalence
classes, after proving they can be obtained as the
orbits of the action of a Lie group on the differentiable
manifold of matrices defining the subsystems the system
consists of and deduce miniversal deformation
Description of characteristic non-hyperinvariant subspaces in GF(2)
Given a square matrix A , an A -invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T ) that commute with A . Shoda's Theorem gives a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces for a nilpotent matrix in GF(2)GF(2). Here we present an explicit construction for all subspaces of this type.Peer ReviewedPostprint (published version
Description of characteristic non-hyperinvariant subspaces in GF(2)
Given a square matrix A , an A -invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T ) that commute with A . Shoda's Theorem gives a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces for a nilpotent matrix in GF(2)GF(2). Here we present an explicit construction for all subspaces of this type.Peer Reviewe
Description of characteristic non-hyperinvariant subspaces over the field GF(2)
Given a square matrix A, an A-invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T) that commute with A. ShodaÊŒs Theorem gives a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces for a nilpotent matrix in GF(2). Here we present an explicit construction for all subspaces of this type.Peer Reviewe
Two parametric quasi-cyclic codes as hyperinvariants subspaces
It is known the relationship between cyclic codes and
invariant subspaces. In this work we present a general-
ization considering âgeneralizedâ cyclic codes and hy-
perinvariant subspace