List questions from invariant-subspace

Published on 25 Mar 2026 - 17:44

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Do there exist two-dimensional subspaces $W$ and $Y$ of $\mathbb{R^4},$ both invariant under $\alpha,$ such that $\mathbb{R^4} = W \oplus Y$?

Published on 29 Mar 2026 - 13:44

152

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Diagonalizability

Published on 30 Apr 2026 - 2:43

370

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Invariant subspaces of vector space.

Published on 25 Mar 2026 - 17:41

38

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Prove $\forall U \subseteq \mathbb R^2\,,\exists \Phi\in \rm{Lin}(\mathbb R^2, \mathbb R^2): null(\Phi) = U$

Published on 09 Nov 2019 - 12:49

145

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Proving that {$v, T(v), ..., T^{n-1}(v)$} is a basis of $ V $

Published on 27 Apr 2026 - 4:43

61

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difference between Cyclic subspace and f-Invariant subspace

Published on 25 Mar 2026 - 19:01

362

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Let $T : \mathbb R^n \rightarrow \mathbb R^m$ is a Linear Transformation. Prove that $\operatorname {im}(T)$ is a subspace of $\Bbb R^m$

Published on 25 Mar 2026 - 17:42

123

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commute operators and invariant subspace on Hardy-Hilbert space

Published on 25 Mar 2026 - 17:45

59

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Invariant Subspace of Vertex Representation of $D_4$

Published on 25 Mar 2026 - 19:04

98

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Invariant subspaces under linear transformation and its complexification

Published on 25 Mar 2026 - 20:41

1k

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Is every invariant subspace also a generalized eigenspace?

Published on 09 Apr 2026 - 13:24

936

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Is every invariant subspace equal to some $\text{null}(T-\lambda I)^n$?

Published on 09 Apr 2026 - 13:24

97

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If exists an Eigenspace $V_{\lambda}$ with dim($V_{\lambda}) \geq 2$, the $f$-invariant subspaces are infinite

Published on 09 Apr 2026 - 13:25

85

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On the space of polynomials in $T$ (a linear operator) with no non-zero invariant subspace

Published on 25 Mar 2026 - 17:40

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Difference between subspace types?

Do there exist two-dimensional subspaces $W$ and $Y$ of $\mathbb{R^4},$ both invariant under $\alpha,$ such that $\mathbb{R^4} = W \oplus Y$?

Diagonalizability

Invariant subspaces of vector space.

Prove $\forall U \subseteq \mathbb R^2\,,\exists \Phi\in \rm{Lin}(\mathbb R^2, \mathbb R^2): null(\Phi) = U$

Proving that {$v, T(v), ..., T^{n-1}(v)$} is a basis of $ V $

difference between Cyclic subspace and f-Invariant subspace

Let $T : \mathbb R^n \rightarrow \mathbb R^m$ is a Linear Transformation. Prove that $\operatorname {im}(T)$ is a subspace of $\Bbb R^m$

commute operators and invariant subspace on Hardy-Hilbert space

Invariant Subspace of Vertex Representation of $D_4$

Invariant subspaces under linear transformation and its complexification

Is every invariant subspace also a generalized eigenspace?

Is every invariant subspace equal to some $\text{null}(T-\lambda I)^n$?

If exists an Eigenspace $V_{\lambda}$ with dim($V_{\lambda}) \geq 2$, the $f$-invariant subspaces are infinite

On the space of polynomials in $T$ (a linear operator) with no non-zero invariant subspace

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