List questions from nilpotence

Published on 23 Nov 2020 - 22:15

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$A$ is nilpotent matrix and satisfies the equation $A^5=3A^3-2A.$ Prove $A=0.$

Published on 03 Dec 2020 - 7:29

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Does strictly upper triangularity of $PAP^{-1}$ imply strictly upper triangularity of $PBP^{-1}$?

Published on 08 Dec 2020 - 12:39

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Proving $3\times3$ nilpotent matrix satisfies $A^3=0$

Published on 11 Dec 2020 - 6:26

299

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Error in my argument that $A^m=0$ implies $A^{m-1}=0$ for matrix $A$?

Published on 17 Dec 2020 - 8:49

407

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Sum of nilpotent matrices with certain property is nilpotent

Published on 17 Dec 2020 - 16:41

57

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$A$ is nilpotent $4\times 4$ matrix and $\ker A^2 \ne \ker A^3$, Prove/Disprove the following

Published on 22 Dec 2020 - 15:02

512

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Atiyah-Macdonald: Exercise 3.5

Published on 22 Dec 2020 - 17:48

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Finding zero divisors of quotient rings $\mathbb{C}[x,y,z]/I$

Published on 12 Jan 2021 - 14:05

122

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When a power of a prime ideal is not a primary Ideal

Published on 15 Jan 2021 - 12:11

201

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Invertibility of $I-A^s$ for each $s \geq 1$ implying nilpotence

Published on 16 Jan 2021 - 4:34

38

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Transforming of a nilpotent matrix to a specific form

Published on 21 Jan 2021 - 9:25

114

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A proof of the Jordan-Chevalley decomposition

Published on 23 Jan 2021 - 15:40

346

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Example of a non-nilpotent linear transformation that for every $v$ gives $A^n(v)=0$ for some $n$

Published on 27 Jan 2021 - 8:01

1.1k

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Find all units, zero divisors and nilpotent elements of $\mathbb{Z}_4[X]$ and $\mathbb{Z}_6[X]$

Published on 30 Jan 2021 - 18:15

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Subset of nilpotent mappings of self maps is not open

$A$ is nilpotent matrix and satisfies the equation $A^5=3A^3-2A.$ Prove $A=0.$

Does strictly upper triangularity of $PAP^{-1}$ imply strictly upper triangularity of $PBP^{-1}$?

Proving $3\times3$ nilpotent matrix satisfies $A^3=0$

Error in my argument that $A^m=0$ implies $A^{m-1}=0$ for matrix $A$?

Sum of nilpotent matrices with certain property is nilpotent

$A$ is nilpotent $4\times 4$ matrix and $\ker A^2 \ne \ker A^3$, Prove/Disprove the following

Atiyah-Macdonald: Exercise 3.5

Finding zero divisors of quotient rings $\mathbb{C}[x,y,z]/I$

When a power of a prime ideal is not a primary Ideal

Invertibility of $I-A^s$ for each $s \geq 1$ implying nilpotence

Transforming of a nilpotent matrix to a specific form

A proof of the Jordan-Chevalley decomposition

Example of a non-nilpotent linear transformation that for every $v$ gives $A^n(v)=0$ for some $n$

Find all units, zero divisors and nilpotent elements of $\mathbb{Z}_4[X]$ and $\mathbb{Z}_6[X]$

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