On the variety of invariant subspaces of a finite-dimensional linear operator
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- by Mark A. Shayman PDF
- Trans. Amer. Math. Soc. 274 (1982), 721-747 Request permission
Abstract:
If $V$ is a finite-dimensional vector space over $\mathbf {R}$ or $\mathbf {C}$ and $A \in {\operatorname {Hom}}(V)$, the set ${S_A}(k)$ of $k$-dimensional $A$-invariant subspaces is a compact subvariety of the Grassmann manifold ${G^k}(V)$, but it need not be a Schubert variety. We study the topology of ${S_A}(k)$. We reduce to the case where $A$ is nilpotent. In this case we prove that ${S_A}(k)$ is connected but need not be a manifold. However, the subset of ${S_A}(k)$ consisting of those subspaces with a fixed cyclic structure is a regular submanifold of ${G^k}(V)$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 274 (1982), 721-747
- MSC: Primary 15A04; Secondary 14M15
- DOI: https://doi.org/10.1090/S0002-9947-1982-0675077-2
- MathSciNet review: 675077