List questions from nilpotence

Published on 07 Jan 2019 - 7:20

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Proof of Jordan-Chevalley decomposition

Published on 10 Jan 2019 - 17:17

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For what values of $b$ are the $4\times 4$ matrices $A$ and $B_b$ similar?

Published on 19 Jan 2019 - 23:55

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Eigenvalues of a matrix whose square is zero

Published on 04 Feb 2019 - 20:00

43

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Let B be a nilpotent linear operator with index p. Is operator $ N^2 + \alpha*N $ nilpotent?

Published on 14 Feb 2019 - 17:02

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2x2 Matrix with no zero entries where $A^k=0$ - Nilpotence?

Published on 17 Feb 2019 - 16:38

89

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k-th power nilpotence ($k\ge 3$)

Published on 19 Feb 2019 - 18:59

98

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Proving that an element is nilpotent

Published on 26 Feb 2019 - 8:36

232

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Usage of Zorn's Lemma to prove that the intersection of all prime ideals contains only nilpotent elements.

Published on 27 Feb 2019 - 0:19

578

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Nilpotent, Idempotent and Involutory Matrix

Published on 25 Mar 2026 - 6:10

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Exericse about linear map $T\in L(V)$, where $\dim V=n\geq2$, with $\operatorname{null}T^{n-1}\neq\operatorname{null}T^n$

Published on 05 Mar 2019 - 1:10

558

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Nilradical is the intersection of finitely many minimal prime ideals.

Published on 11 Mar 2019 - 6:34

147

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Determine all $2 \times 2$ real matrices $A$ such that $(1) \ \ A^2=I$, $(2) \ \ A^2=0$

Published on 17 Mar 2019 - 13:42

1.3k

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If $B$ is nilpotent and $AB=BA$ then $\det(A+B) = \det(A)$

Published on 23 Mar 2019 - 14:14

86

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nilpotent endomorphism and $Im(f)+Ker(f) \neq dim(V)$

Published on 24 Mar 2019 - 15:50

List Question

$A$ nilpotent and $A+c_iB$ is nilpotent then $B$ is nilpotent.

Proof of Jordan-Chevalley decomposition

For what values of $b$ are the $4\times 4$ matrices $A$ and $B_b$ similar?

Eigenvalues of a matrix whose square is zero

Let B be a nilpotent linear operator with index p. Is operator $ N^2 + \alpha*N $ nilpotent?

2x2 Matrix with no zero entries where $A^k=0$ - Nilpotence?

k-th power nilpotence ($k\ge 3$)

Proving that an element is nilpotent

Usage of Zorn's Lemma to prove that the intersection of all prime ideals contains only nilpotent elements.

Nilpotent, Idempotent and Involutory Matrix

Exericse about linear map $T\in L(V)$, where $\dim V=n\geq2$, with $\operatorname{null}T^{n-1}\neq\operatorname{null}T^n$

Nilradical is the intersection of finitely many minimal prime ideals.

Determine all $2 \times 2$ real matrices $A$ such that $(1) \ \ A^2=I$, $(2) \ \ A^2=0$

If $B$ is nilpotent and $AB=BA$ then $\det(A+B) = \det(A)$

nilpotent endomorphism and $Im(f)+Ker(f) \neq dim(V)$

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