List questions from nilpotence

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Which of the following options must be true.

Published on 28 Aug 2021 - 2:36

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What does it mean that lower central series terminate?

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Let $A \in M_n(C)$, $A^m = 0 \implies A^n = 0$

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Proof of Nilpotency of Matrix All Whose Powers Have Vanishing Trace Without Using Eigenvalues

Published on 08 Sep 2021 - 14:19

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Lower central series of the Unitriangular group $UT(n, \mathbb{Z}_p)$

Published on 26 Mar 2026 - 6:30

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Hoffman Kunze Section 6.8 Exercise 12

Published on 25 Mar 2026 - 14:21

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Why is A not 1 nilpotent?

Published on 04 Mar 2026 - 2:46

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A nilpotent element in $\mathbb{Z}/ 96\mathbb{Z}$

Published on 15 Oct 2021 - 19:57

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Nilpotent Operators over Vector Spaces

Published on 16 Oct 2021 - 18:48

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Norm of complex symmetric nilpotent matrix

Published on 27 Oct 2021 - 12:50

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$R[x]$ is semiprimitive if and only if $R$ has no non-zero nilpotent ideals

Published on 03 Nov 2021 - 7:42

193

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Let $ T: V \to V $ be nilpotent. Let $ f \in \mathbb{F[x]}. $ Show that $ f(T) $ is invertible iff $ f(0) \neq 0 $

Published on 12 Nov 2021 - 9:41

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$ N$ is nilpotent and $ T $ is diagonalizable transformation s.t. $ N \circ T = T \circ N $. Show $ \ker q_{\lambda} ( T + N ) = V_{\lambda} $

Published on 14 Nov 2021 - 12:24

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Linear algebra: nilpotent matrix and determinant.

Published on 15 Nov 2021 - 15:12

List Question

Let $A_{n×n}$ be a complex matrix then prove that $ch_{AB}(x) = ch_{BA}(x)$

Which of the following options must be true.

What does it mean that lower central series terminate?

Let $A \in M_n(C)$, $A^m = 0 \implies A^n = 0$

Proof of Nilpotency of Matrix All Whose Powers Have Vanishing Trace Without Using Eigenvalues

Lower central series of the Unitriangular group $UT(n, \mathbb{Z}_p)$

Hoffman Kunze Section 6.8 Exercise 12

Why is A not 1 nilpotent?

A nilpotent element in $\mathbb{Z}/ 96\mathbb{Z}$

Nilpotent Operators over Vector Spaces

Norm of complex symmetric nilpotent matrix

$R[x]$ is semiprimitive if and only if $R$ has no non-zero nilpotent ideals

Let $ T: V \to V $ be nilpotent. Let $ f \in \mathbb{F[x]}. $ Show that $ f(T) $ is invertible iff $ f(0) \neq 0 $

$ N$ is nilpotent and $ T $ is diagonalizable transformation s.t. $ N \circ T = T \circ N $. Show $ \ker q_{\lambda} ( T + N ) = V_{\lambda} $

Linear algebra: nilpotent matrix and determinant.

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