Description of characteristic non-hyperinvariant subspaces over the field GF(2)

作者：Mingueza David; Eulalia Montoro M; Pacha Juan R

来源：Linear Algebra and Its Applications, 2013, 439(12): 3734-3745.

DOI：10.1016/j.laa.2013.10.025

• Hyperinvariant subspaces
• Characteristic subspaces
• Shoda%26apos
• s Theorem

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%26apos;s 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.

• 出版日期2013-12-15