Question

Polynomial of linear transformation

score 60 · Answer 1 · 2026-04-09 17:24:53

60

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Polynomial of linear transformation

Published on 09 Apr 2026 - 17:24

score 252 · Answer 2 · 2026-04-14 06:24:04

252

Views

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

Published on 14 Apr 2026 - 6:24

score 815 · Answer 3 · 2026-05-04 18:25:11

815

Views

Proof of Existence of Decomposition of a Vector Space

Published on 04 May 2026 - 18:25

score 446 · Answer 4 · 2026-04-17 07:10:49

446

Views

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

Published on 17 Apr 2026 - 7:10

score 42 · Answer 5 · 2026-04-13 03:24:13

42

Views

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

Published on 13 Apr 2026 - 3:24

score 1.1k · Answer 6 · 2026-04-17 07:30:21

1.1k

Views

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

Published on 17 Apr 2026 - 7:30

score 1.5k · Answer 7 · 2026-04-14 06:54:57

1.5k

Views

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

Published on 14 Apr 2026 - 6:54

score 71 · Answer 8 · 2026-04-15 20:55:33

71

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

Published on 15 Apr 2026 - 20:55

score 420 · Answer 9 · 2026-05-10 07:50:56

420

Views

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

Published on 10 May 2026 - 7:50

score 129 · Answer 10 · 2026-04-07 21:53:57

129

Views

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

Published on 07 Apr 2026 - 21:53

score 1k · Answer 11 · 2026-04-15 20:30:26

1k

Views

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 Apr 2026 - 20:30

score 1.2k · Answer 12 · 2026-04-16 18:53:36

1.2k

Views

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

Published on 16 Apr 2026 - 18:53

score 243 · Answer 13 · 2026-04-12 20:11:00

243

Views

Proving existence of common eigenvalue using invariant subspace properties

Published on 12 Apr 2026 - 20:11

score 439 · Answer 14 · 2026-04-16 02:34:42

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 214 · Answer 15 · 2026-04-11 07:49:51

214

Views

Transformation restriction to commutative matrices

Published on 11 Apr 2026 - 7:49

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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