Question

prove that if $A^k =0$ then there is $v \in \mathbb{F}^{n}$ such that the group $\{v,vA,vA^2,\dots,vA^{k-1}\}$ is linearly independent in induction

score 67 · Answer 1 · 2026-02-23 15:18:49

67

Views

prove that if $A^k =0$ then there is $v \in \mathbb{F}^{n}$ such that the group $\{v,vA,vA^2,\dots,vA^{k-1}\}$ is linearly independent in induction

Published on 23 Feb 2026 - 15:18

score 107 · Answer 2 · 2024-03-20 08:51:43

107

Views

Is this method for constructing nilpotent matrices effective?

Published on 20 Mar 2024 - 8:51

score 123 · Answer 3 · 2015-01-06 15:01:14

123

Views

Are commuting endomorphisms polynomials of a same (third) endomorphism?

Published on 06 Jan 2015 - 15:01

score 28 · Answer 4 · 2015-01-08 08:57:41

28

Views

About hermiticity implying non-nilpotency for infinite dimensional vector space(Corrected)

Published on 08 Jan 2015 - 8:57

score 294 · Answer 5 · 2015-01-12 22:19:35

294

Views

Bound number of generators of a subgroup of a nilpotent group?

Published on 12 Jan 2015 - 22:19

score 675 · Answer 6 · 2015-01-15 20:45:41

675

Views

Find diagonalizable and nilpotent parts of matrix

Published on 15 Jan 2015 - 20:45

score 1.2k · Answer 7 · 2015-01-16 22:28:45

1.2k

Views

nilpotent elements of $M_2(\mathbb{R})$, $M_2(\mathbb{Z}/4\mathbb{Z})$

Published on 16 Jan 2015 - 22:28

score 416 · Answer 8 · 2015-01-17 19:48:29

416

Views

Given A is a nil-potent matrix (given $ A^k=0 $), prove that A-I is invertible. Is my proof correct?

Published on 17 Jan 2015 - 19:48

score 1.3k · Answer 9 · 2015-01-22 01:27:25

1.3k

Views

Some solvable Lie algebra but not nilpotent

Published on 22 Jan 2015 - 1:27

score 140 · Answer 10 · 2015-01-24 09:01:04

140

Views

Rings with bounded index of nilpotency are Dedekind-Finite

Published on 24 Jan 2015 - 9:01

score 765 · Answer 11 · 2015-02-01 20:24:41

765

Views

An example of a nilpotent group

Published on 01 Feb 2015 - 20:24

score 3.7k · Answer 12 · 2015-02-05 06:57:39

3.7k

Views

Decompose this matrix as a sum of unit and nilpotent matrix.

Published on 05 Feb 2015 - 6:57

score 1.7k · Answer 13 · 2015-02-09 03:38:05

1.7k

Views

Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.

Published on 09 Feb 2015 - 3:38

score 300 · Answer 14 · 2015-02-11 22:14:08

300

Views

Is $A$ nilpotent matrix?

Published on 11 Feb 2015 - 22:14

score 532 · Answer 15 · 2015-02-12 04:41:16

532

Views

If $A$ is nilpotent, why is $A$ non-invertible?

Published on 12 Feb 2015 - 4:41

List Question

prove that if $A^k =0$ then there is $v \in \mathbb{F}^{n}$ such that the group $\{v,vA,vA^2,\dots,vA^{k-1}\}$ is linearly independent in induction

Is this method for constructing nilpotent matrices effective?

Are commuting endomorphisms polynomials of a same (third) endomorphism?

About hermiticity implying non-nilpotency for infinite dimensional vector space(Corrected)

Bound number of generators of a subgroup of a nilpotent group?

Find diagonalizable and nilpotent parts of matrix

nilpotent elements of $M_2(\mathbb{R})$, $M_2(\mathbb{Z}/4\mathbb{Z})$

Given A is a nil-potent matrix (given $ A^k=0 $), prove that A-I is invertible. Is my proof correct?

Some solvable Lie algebra but not nilpotent

Rings with bounded index of nilpotency are Dedekind-Finite

An example of a nilpotent group

Decompose this matrix as a sum of unit and nilpotent matrix.

Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.

Is $A$ nilpotent matrix?

If $A$ is nilpotent, why is $A$ non-invertible?

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