List questions from nilpotence

Published on 10 Dec 2019 - 14:09

143

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Non-zero nilpotent operator

Published on 11 Dec 2019 - 9:42

172

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T ∈ L(V) is nilpotent if and only if σ(T) = {0}.

Published on 11 Dec 2019 - 10:50

137

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Give an example of an operator $T \in L(\mathbb C^7,\mathbb C^7)$ such that $T^2+T+I$ is nilpotent.

Published on 12 Dec 2019 - 22:41

700

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Proving by induction that strictly lower triangular matrix is nilpotent

Published on 15 Dec 2019 - 11:10

309

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Examples for commutative rings with many nilpotent elements yet the nilradical is not

Published on 25 Dec 2019 - 21:53

102

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$n$-th power of a matrix

Published on 28 Dec 2019 - 8:37

166

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Prove that $A$ and $B$ are nilpotent - proof checking

Published on 29 Dec 2019 - 17:36

622

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What can be said about the rank of a nilpotent matrix?

Published on 30 Dec 2019 - 18:20

3.1k

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Index of a Nilpotent matrix

Published on 25 Mar 2026 - 19:45

105

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Strange result on the nilradical $N(R)$ of a ring

Published on 08 Jan 2020 - 23:18

135

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Proving that $N(R)\times N(S)= N(R\times S)$

Published on 09 Jan 2020 - 0:13

71

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In every local ring exist nonzero nilpotent ideals?

Published on 12 Jan 2020 - 0:54

117

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Inverse of $I + A$

Published on 17 Jan 2020 - 0:48

168

Views

Is an ideal where all elements have $x^m=0$ nilpotent?

Published on 28 Jan 2020 - 16:02

List Question

Prove that there exist a diagonalizable operator $D$ and a nilpotent operator $N$

Non-zero nilpotent operator

T ∈ L(V) is nilpotent if and only if σ(T) = {0}.

Give an example of an operator $T \in L(\mathbb C^7,\mathbb C^7)$ such that $T^2+T+I$ is nilpotent.

Proving by induction that strictly lower triangular matrix is nilpotent

Examples for commutative rings with many nilpotent elements yet the nilradical is not

$n$-th power of a matrix

Prove that $A$ and $B$ are nilpotent - proof checking

What can be said about the rank of a nilpotent matrix?

Index of a Nilpotent matrix

Strange result on the nilradical $N(R)$ of a ring

Proving that $N(R)\times N(S)= N(R\times S)$

In every local ring exist nonzero nilpotent ideals?

Inverse of $I + A$

Is an ideal where all elements have $x^m=0$ nilpotent?

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