On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result) (Q5935586)
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scientific article; zbMATH DE number 1610680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result) |
scientific article; zbMATH DE number 1610680 |
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On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result) (English)
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1 April 2003
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invariant subspace
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commutant
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functor
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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)]. NEWLINENEWLINENEWLINEIn the paper under review, this fact is proved using some basic ideas belonging to the structure theory of Abelian groups.
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