Question

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

score 64 · Answer 1 · 2018-12-04 11:52:24

64

Views

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

Published on 04 Dec 2018 - 11:52

score 63 · Answer 2 · 2018-12-10 21:33:00

63

Views

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

Published on 10 Dec 2018 - 21:33

score 379 · Answer 3 · 2018-12-12 07:11:45

379

Views

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

Published on 12 Dec 2018 - 7:11

score 79 · Answer 4 · 2018-12-15 14:51:44

79

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 15 Dec 2018 - 14:51

score 49 · Answer 5 · 2018-12-16 15:29:37

49

Views

Invariant subspace concept - generalization

Published on 16 Dec 2018 - 15:29

score 205 · Answer 6 · 2018-12-17 04:47:47

205

Views

Application of the cyclic decomposition theorem to a linear transformation

Published on 17 Dec 2018 - 4:47

score 654 · Answer 7 · 2019-01-13 10:39:37

654

Views

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

Published on 13 Jan 2019 - 10:39

score 225 · Answer 8 · 2019-01-24 15:07:36

225

Views

Is this representation completely reducible?

Published on 24 Jan 2019 - 15:07

score 70 · Answer 9 · 2019-01-26 23:56:50

70

Views

Finding all subspaces invariant under F.

Published on 26 Jan 2019 - 23:56

score 48 · Answer 10 · 2019-01-30 16:59:15

48

Views

Finding all subspaces invariant under F.(2)

Published on 30 Jan 2019 - 16:59

score 72 · Answer 11 · 2019-02-05 02:53:22

72

Views

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

Published on 05 Feb 2019 - 2:53

score 215 · Answer 12 · 2019-02-17 23:33:08

215

Views

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

Published on 17 Feb 2019 - 23:33

score 192 · Answer 13 · 2019-02-22 15:41:43

192

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 22 Feb 2019 - 15:41

score 101 · Answer 14 · 2019-02-26 18:26:37

101

Views

What if there are two non-orthogonal invariant subspaces?

Published on 26 Feb 2019 - 18:26

score 130 · Answer 15 · 2019-03-02 09:28:19

130

Views

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

Published on 02 Mar 2019 - 9:28

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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