On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result)
Copyright policy )On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result)
The fact that for any linear operator \(A\) on a finite-dimensional complex vector space, the lattice of invariant subspaces of \(A\) coincides with the set of ranges of the operators which commute with \(A\), was pointed out by \textit{P. R. Halmos} [Linear Algebra Appl. 4, 11-15 (1971; Zbl 0264.15001)]. In the paper under review, this fact is proved using some basic ideas belonging to the structure theory of Abelian groups.
- Chouaib Doukkali University Morocco
Functor, Numerical Analysis, Invariant subspaces of linear operators, Algebra and Number Theory, Invariant subspaces, commutant, invariant subspace, Discrete Mathematics and Combinatorics, Geometry and Topology, functor, Commutant, Abelian groups
Functor, Numerical Analysis, Invariant subspaces of linear operators, Algebra and Number Theory, Invariant subspaces, commutant, invariant subspace, Discrete Mathematics and Combinatorics, Geometry and Topology, functor, Commutant, Abelian groups
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