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Exercise on finding nilpotent elements

score 57 · Answer 1 · 2021-05-26 21:36:51

57

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Exercise on finding nilpotent elements

Published on 26 May 2021 - 21:36

score 101 · Answer 2 · 2021-05-28 16:00:21

101

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A problem nilpotent linear operator

Published on 28 May 2021 - 16:00

score 104 · Answer 3 · 2021-05-28 20:54:02

104

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$A \in GL_n (\mathbb C)$ and $N$ nilpotent matrix, A and N commute. Show there exists B such as $B^{2} = A + N$

Published on 28 May 2021 - 20:54

score 44 · Answer 4 · 2021-05-29 18:15:33

44

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Prove that if ${\frak g}\le{\frak gl}(V)$ and $\mathfrak h\le\mathfrak g$ is a maximal subalgebra, then $\mathfrak h$ is an ideal of codimension $1$

Published on 29 May 2021 - 18:15

score 68 · Answer 5 · 2021-06-06 19:30:32

68

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Find $\{X^{T}AX:X \in\mathbb{R}^n\}$ where $A$ is nilpotent.

Published on 06 Jun 2021 - 19:30

score 224 · Answer 6 · 2021-06-06 23:14:07

224

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Proving that $\det(A+N) = 0$ with N a nilpotent matrix and A a singular matrix such that AN=NA

Published on 06 Jun 2021 - 23:14

score 515 · Answer 7 · 2021-06-10 15:14:24

515

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Help with Nilpotent Transformation Proof

Published on 10 Jun 2021 - 15:14

score 309 · Answer 8 · 2021-06-10 22:19:44

309

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Does a nilpotent operator always have a Jordan representation?

Published on 10 Jun 2021 - 22:19

score 311 · Answer 9 · 2021-06-14 12:34:03

311

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Does every nilpotent element in a real Lie algebra lie in some minimal parabolic Lie algebra?

Published on 14 Jun 2021 - 12:34

score 319 · Answer 10 · 2021-07-13 15:18:46

319

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$\mathfrak{Jac}(A[x])=\mathfrak{Nil}(A[x])$

Published on 13 Jul 2021 - 15:18

score 518 · Answer 11 · 2021-08-14 15:14:04

518

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Why do successive compositions of nilpotent operators strictly decrease their rank?

Published on 14 Aug 2021 - 15:14

score 318 · Answer 12 · 2026-03-25 23:38:19

318

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If $A\in M_n(\mathbb{C})$ is a nilpotent matrix then $A$ is similar to $2A$

Published on 25 Mar 2026 - 23:38

score 72 · Answer 13 · 2021-08-18 09:45:04

72

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How to construct nilpotent of order $3$

Published on 18 Aug 2021 - 9:45

score 332 · Answer 14 · 2021-08-23 12:59:49

332

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Nilpotent elements of $R$: If $x \in \operatorname{Nil}(R)$ then $1+x \notin P$, where $P$ is any prime ideal of $R$.

Published on 23 Aug 2021 - 12:59

score 116 · Answer 15 · 2026-03-26 04:51:42

116

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An association between finite nilpotent groups and Lie rings

Published on 26 Mar 2026 - 4:51

List Question

Exercise on finding nilpotent elements

A problem nilpotent linear operator

$A \in GL_n (\mathbb C)$ and $N$ nilpotent matrix, A and N commute. Show there exists B such as $B^{2} = A + N$

Prove that if ${\frak g}\le{\frak gl}(V)$ and $\mathfrak h\le\mathfrak g$ is a maximal subalgebra, then $\mathfrak h$ is an ideal of codimension $1$

Find $\{X^{T}AX:X \in\mathbb{R}^n\}$ where $A$ is nilpotent.

Proving that $\det(A+N) = 0$ with N a nilpotent matrix and A a singular matrix such that AN=NA

Help with Nilpotent Transformation Proof

Does a nilpotent operator always have a Jordan representation?

Does every nilpotent element in a real Lie algebra lie in some minimal parabolic Lie algebra?

$\mathfrak{Jac}(A[x])=\mathfrak{Nil}(A[x])$

Why do successive compositions of nilpotent operators strictly decrease their rank?

If $A\in M_n(\mathbb{C})$ is a nilpotent matrix then $A$ is similar to $2A$

How to construct nilpotent of order $3$

Nilpotent elements of $R$: If $x \in \operatorname{Nil}(R)$ then $1+x \notin P$, where $P$ is any prime ideal of $R$.

An association between finite nilpotent groups and Lie rings

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