Question

Polynomial of linear transformation

score 57 · Answer 1 · 2026-03-22 07:58:12

57

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Polynomial of linear transformation

Published on 22 Mar 2026 - 7:58

score 251 · Answer 2 · 2026-03-24 23:46:28

251

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Every $k$ dimensional subspace is $S$-invariant implies $S$ is a multiple of the identity

Published on 24 Mar 2026 - 23:46

score 808 · Answer 3 · 2018-05-17 07:05:40

808

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Proof of Existence of Decomposition of a Vector Space

Published on 17 May 2018 - 7:05

score 443 · Answer 4 · 2018-05-22 23:55:55

443

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Why are there two non-trivial T-invariant subspaces and why the restriction to T is cyclic?

Published on 22 May 2018 - 23:55

score 39 · Answer 5 · 2026-03-22 18:46:10

39

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Proving T-Invariant Subspace not $K^{2}$

Published on 22 Mar 2026 - 18:46

score 1.1k · Answer 6 · 2018-06-03 13:10:45

1.1k

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Any non-trivial $T$-invariant subspace of $V$ contains an eigenvector of $T.$

Published on 03 Jun 2018 - 13:10

score 1.5k · Answer 7 · 2018-06-04 04:11:19

1.5k

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Restriction of a diagonalizable linear operator $T$ to any nontrivial $T$-invariant subspace is also diagonalizable using a given lemma.

Published on 04 Jun 2018 - 4:11

score 68 · Answer 8 · 2018-06-24 17:36:52

68

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Show that there is a k dimensional subspace E such that....

Published on 24 Jun 2018 - 17:36

score 411 · Answer 9 · 2026-03-22 22:32:22

411

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Can one describe the algebraic multiplicity in terms of generalized eigenspaces and the minimal polynomial?

Published on 22 Mar 2026 - 22:32

score 127 · Answer 10 · 2018-07-15 23:10:43

127

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Compact operator on invariant subspace (not necessarily closed) is compact

Published on 15 Jul 2018 - 23:10

score 1k · Answer 11 · 2018-07-15 23:15:21

1k

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For $A\in\mathbb{R}^{n\times n}$ and $B\in\mathbb{R}^{n\times k}$, does $(I_{n}-aA)^{-1}Bb$ determine $a\in\mathbb{R}$ and $b\in\mathbb{R}^k$?

Published on 15 Jul 2018 - 23:15

score 1.2k · Answer 12 · 2018-07-16 08:12:28

1.2k

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Prove that $W$ is $g(T)$-invariant for any polynomial $g(t)$.

Published on 16 Jul 2018 - 8:12

score 240 · Answer 13 · 2018-07-27 17:17:54

240

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Proving existence of common eigenvalue using invariant subspace properties

Published on 27 Jul 2018 - 17:17

score 436 · Answer 14 · 2018-07-30 06:48:16

If $W$ is $T$-invariant space of $V$ and $\left\{0\right\}\ne W\subseteq V$ then $\exists\ w\in W$ such that $w$ is an eigenvector of $T$

score 211 · Answer 15 · 2026-03-22 14:12:41

211

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Transformation restriction to commutative matrices

Published on 22 Mar 2026 - 14:12

List Question

Polynomial of linear transformation

Every $k$ dimensional subspace is $S$-invariant implies $S$ is a multiple of the identity

Proof of Existence of Decomposition of a Vector Space

Why are there two non-trivial T-invariant subspaces and why the restriction to T is cyclic?

Proving T-Invariant Subspace not $K^{2}$

Any non-trivial $T$-invariant subspace of $V$ contains an eigenvector of $T.$

Restriction of a diagonalizable linear operator $T$ to any nontrivial $T$-invariant subspace is also diagonalizable using a given lemma.

Show that there is a k dimensional subspace E such that....

Can one describe the algebraic multiplicity in terms of generalized eigenspaces and the minimal polynomial?

Compact operator on invariant subspace (not necessarily closed) is compact

For $A\in\mathbb{R}^{n\times n}$ and $B\in\mathbb{R}^{n\times k}$, does $(I_{n}-aA)^{-1}Bb$ determine $a\in\mathbb{R}$ and $b\in\mathbb{R}^k$?

Prove that $W$ is $g(T)$-invariant for any polynomial $g(t)$.

Proving existence of common eigenvalue using invariant subspace properties

If $W$ is $T$-invariant space of $V$ and $\left\{0\right\}\ne W\subseteq V$ then $\exists\ w\in W$ such that $w$ is an eigenvector of $T$

Transformation restriction to commutative matrices

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