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 “generalized” 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 A∈Mn(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 A∈Mn(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. Shodaʼs 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 “generalized” cyclic codes and hy- perinvariant subspace