Question

Clarification regarding the number of Jordan blocks of some specific order

score 160 · Answer 1 · 2021-11-15 23:44:51

160

Views

Clarification regarding the number of Jordan blocks of some specific order

Published on 15 Nov 2021 - 23:44

score 48 · Answer 2 · 2021-12-06 07:13:20

48

Views

When does superdiagonal matrix have a single Jordan block

Published on 06 Dec 2021 - 7:13

score 109 · Answer 3 · 2026-03-27 13:48:19

109

Views

If $N^n=0$ but $N^{n-1}\neq 0$, then there is no $n\times n$ matrix $A$ such that $A^2=N$

Published on 27 Mar 2026 - 13:48

score 51 · Answer 4 · 2021-12-21 16:01:16

51

Views

$T \in \text{Hom}V $ is nilpotent implies $I - T$ invertible

Published on 21 Dec 2021 - 16:01

score 194 · Answer 5 · 2022-01-02 03:09:47

194

Views

If a Lie algebra $\mathfrak{g}$ with only one Cartan subalgebra, then can we implies that $\mathfrak{g}$ is nilpotent?

Published on 02 Jan 2022 - 3:09

score 212 · Answer 6 · 2022-01-08 12:09:46

212

Views

Construct a $2022\times 2022$ matrix $A$ such that $A^{2022}=0$ but $A^{2021} \neq 0$

Published on 08 Jan 2022 - 12:09

score 146 · Answer 7 · 2026-03-28 03:27:39

146

Views

Is it possible for $AA^T$ to be a nilpotent matrix if neither $A$ nor $A^T$ are?

Published on 28 Mar 2026 - 3:27

score 688 · Answer 8 · 2022-01-29 12:48:53

688

Views

if $ \dim \ker T^{k-1} < n , \dim \ker T^k = n $ and $ \dim V=n $ then $T$ is nilpotent

Published on 29 Jan 2022 - 12:48

score 205 · Answer 9 · 2022-04-05 03:27:18

205

Views

Prove if $T$ is nilpotent, $ST=TS$, and $\dim\operatorname{Nul}T=2$, then $S$ has at most $2$ distinct eigenvalues

Published on 05 Apr 2022 - 3:27

score 72 · Answer 10 · 2022-04-28 17:25:29

72

Views

What is the index of nilpotency of $A$?

Published on 28 Apr 2022 - 17:25

score 98 · Answer 11 · 2022-05-10 14:12:49

98

Views

Kernel and image of a nilpotent linear map

Published on 10 May 2022 - 14:12

score 115 · Answer 12 · 2022-05-16 01:13:26

115

Views

Does $AX+XB=B$ have a unique solution?

Published on 16 May 2022 - 1:13

score 73 · Answer 13 · 2022-05-27 01:01:38

73

Views

Constructing pairwise commuting nilpotent matrices

Published on 27 May 2022 - 1:01

score 39 · Answer 14 · 2022-06-02 19:18:53

39

Views

Unipotent and semisimple elements are locally finite

Published on 02 Jun 2022 - 19:18

score 68 · Answer 15 · 2026-03-21 23:52:49

68

Views

If $A$ has no non-trivial idempotents, then neither does $A/N$

Published on 21 Mar 2026 - 23:52

List Question

Clarification regarding the number of Jordan blocks of some specific order

When does superdiagonal matrix have a single Jordan block

If $N^n=0$ but $N^{n-1}\neq 0$, then there is no $n\times n$ matrix $A$ such that $A^2=N$

$T \in \text{Hom}V $ is nilpotent implies $I - T$ invertible

If a Lie algebra $\mathfrak{g}$ with only one Cartan subalgebra, then can we implies that $\mathfrak{g}$ is nilpotent?

Construct a $2022\times 2022$ matrix $A$ such that $A^{2022}=0$ but $A^{2021} \neq 0$

Is it possible for $AA^T$ to be a nilpotent matrix if neither $A$ nor $A^T$ are?

if $ \dim \ker T^{k-1} < n , \dim \ker T^k = n $ and $ \dim V=n $ then $T$ is nilpotent

Prove if $T$ is nilpotent, $ST=TS$, and $\dim\operatorname{Nul}T=2$, then $S$ has at most $2$ distinct eigenvalues

What is the index of nilpotency of $A$?

Kernel and image of a nilpotent linear map

Does $AX+XB=B$ have a unique solution?

Constructing pairwise commuting nilpotent matrices

Unipotent and semisimple elements are locally finite

If $A$ has no non-trivial idempotents, then neither does $A/N$

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