Question

Prove that if $\phi$ is invertible operator of V space, then $\phi$ and $\phi^{-1}$ has the same invariant subspaces.

score 66 · Answer 1 · 2026-04-15 13:48:20

66

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Prove that if $\phi$ is invertible operator of V space, then $\phi$ and $\phi^{-1}$ has the same invariant subspaces.

Published on 15 Apr 2026 - 13:48

score 66 · Answer 2 · 2026-04-15 08:38:11

66

Views

Is the set of all vectors in the span of $\pmatrix{1 \\ 2}$ and $\pmatrix{2 \\ -1}$ a subspace or not?

Published on 15 Apr 2026 - 8:38

score 382 · Answer 3 · 2026-04-09 22:58:31

382

Views

How to represent characteristic polynomial in terms of those of invariant direct sum subspaces?

Published on 09 Apr 2026 - 22:58

score 82 · Answer 4 · 2026-04-14 23:30:19

82

Views

$T$ and $U$ have a common eigenvector, where $T$ and $U$ are linear operators on odd dimensional vector space $V$ and $T^2 = U^2 = I$.

Published on 14 Apr 2026 - 23:30

score 52 · Answer 5 · 2026-04-15 03:16:12

52

Views

Invariant subspace concept - generalization

Published on 15 Apr 2026 - 3:16

score 208 · Answer 6 · 2026-04-11 18:59:35

208

Views

Application of the cyclic decomposition theorem to a linear transformation

Published on 11 Apr 2026 - 18:59

score 657 · Answer 7 · 2026-04-16 12:32:44

657

Views

Let $v_1$, $v_2$, $v_3$ be a basis of the $\mathbb{R}$-vector space $\mathbb{R}^3$

Published on 16 Apr 2026 - 12:32

score 229 · Answer 8 · 2026-04-12 02:04:03

229

Views

Is this representation completely reducible?

Published on 12 Apr 2026 - 2:04

score 74 · Answer 9 · 2026-04-15 20:26:38

74

Views

Finding all subspaces invariant under F.

Published on 15 Apr 2026 - 20:26

score 51 · Answer 10 · 2026-04-15 02:35:43

51

Views

Finding all subspaces invariant under F.(2)

Published on 15 Apr 2026 - 2:35

score 76 · Answer 11 · 2026-04-12 07:03:01

76

Views

Why is $\mathcal{K}$ invariant under $A$?

Published on 12 Apr 2026 - 7:03

score 218 · Answer 12 · 2026-04-15 22:40:07

218

Views

Prove that the image of an invariant subspace under a morphism of representations is an invariant subspace.

Published on 15 Apr 2026 - 22:40

score 196 · Answer 13 · 2026-04-15 20:29:00

196

Views

Finding the submodules of the $\mathbb{R}[x]$-module defined by $A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 &0 & -1 \end{bmatrix} $

Published on 15 Apr 2026 - 20:29

score 104 · Answer 14 · 2026-04-15 14:32:52

104

Views

What if there are two non-orthogonal invariant subspaces?

Published on 15 Apr 2026 - 14:32

score 135 · Answer 15 · 2026-04-17 14:34:11

135

Views

Does the action of a linear map on $k$-dimensional subspaces determine it up to scaling?

Published on 17 Apr 2026 - 14:34

List Question

Prove that if $\phi$ is invertible operator of V space, then $\phi$ and $\phi^{-1}$ has the same invariant subspaces.

Is the set of all vectors in the span of $\pmatrix{1 \\ 2}$ and $\pmatrix{2 \\ -1}$ a subspace or not?

How to represent characteristic polynomial in terms of those of invariant direct sum subspaces?

$T$ and $U$ have a common eigenvector, where $T$ and $U$ are linear operators on odd dimensional vector space $V$ and $T^2 = U^2 = I$.

Invariant subspace concept - generalization

Application of the cyclic decomposition theorem to a linear transformation

Let $v_1$, $v_2$, $v_3$ be a basis of the $\mathbb{R}$-vector space $\mathbb{R}^3$

Is this representation completely reducible?

Finding all subspaces invariant under F.

Finding all subspaces invariant under F.(2)

Why is $\mathcal{K}$ invariant under $A$?

Prove that the image of an invariant subspace under a morphism of representations is an invariant subspace.

Finding the submodules of the $\mathbb{R}[x]$-module defined by $A=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 &0 & -1 \end{bmatrix} $

What if there are two non-orthogonal invariant subspaces?

Does the action of a linear map on $k$-dimensional subspaces determine it up to scaling?

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