Question

If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.

score 53.4k · Answer 1 · 2015-04-15 18:10:59

53.4k

Views

If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.

Published on 15 Apr 2015 - 18:10

score 138 · Answer 2 · 2015-04-19 18:37:16

138

Views

Exercise on linear maps with a nilpotent one

Published on 19 Apr 2015 - 18:37

score 75 · Answer 3 · 2015-04-24 11:24:07

75

Views

Degree $2$ nilpotent matrices with non-zero product and subset products not depending on the order

Published on 24 Apr 2015 - 11:24

score 402 · Answer 4 · 2015-04-25 20:19:33

402

Views

nilpotent algebraic groups in terms of extensions

Published on 25 Apr 2015 - 20:19

score 143 · Answer 5 · 2015-04-27 20:18:40

143

Views

Matrix representations and idempotent/nilpotent elements

Published on 27 Apr 2015 - 20:18

score 90 · Answer 6 · 2015-05-03 10:40:24

90

Views

On a question about nilpotent matrices

Published on 03 May 2015 - 10:40

score 46.5k · Answer 7 · 2015-05-04 02:33:47

46.5k

Views

Why are eigenvalues of nilpotent matrices equal to zero?

Published on 04 May 2015 - 2:33

score 1.8k · Answer 8 · 2015-05-04 03:11:47

1.8k

Views

Finding a non-zero vector in both the column space and the null space of a nilpotent matrix

Published on 04 May 2015 - 3:11

score 84 · Answer 9 · 2015-05-04 03:48:10

84

Views

Prove that $ \text{rank}(A^{3}) < \text{rank}(A^{2}) < \text{rank}(A) $ if $ A $ is a $ (10 \times 10) $-matrix with nilpotence equal to $ 3 $.

Published on 04 May 2015 - 3:48

score 153 · Answer 10 · 2015-05-08 08:30:00

153

Views

Carter Subgroups and Projectors

Published on 08 May 2015 - 8:30

score 2.2k · Answer 11 · 2015-05-13 17:41:29

2.2k

Views

Nilpotent matrices: is there a fast trick to find the degree?

Published on 13 May 2015 - 17:41

score 154 · Answer 12 · 2015-05-19 13:21:05

154

Views

Find endomorphisms $α$ and $β$ of $V$ satisfying the condition that $αβ$ is not nilpotent but $cα+dβ$ is nilpotent for all $c, d ∈ \mathbb{R}$

Published on 19 May 2015 - 13:21

score 285 · Answer 13 · 2015-05-20 01:42:33

285

Views

Let $V$ be a vector space and $\alpha$ a nilpotent endomorfism (of degree $k$), how can I show that $\alpha(x)+x$ is epic?

Published on 20 May 2015 - 1:42

score 132 · Answer 14 · 2015-05-20 02:52:51

132

Views

Let $\dim(V)<\infty$ . Do there exist endomorphisms of $V$ satisfying the condition that $σ_1 + αβ − βα$ is nilpotent?

Published on 20 May 2015 - 2:52

score 1.3k · Answer 15 · 2015-05-25 18:30:55

1.3k

Views

The number of $3\times 3$ nilpotent matrices over $\mathbb{F}_q$ using the orbit-stabilizer theorem

Published on 25 May 2015 - 18:30

List Question

If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.

Exercise on linear maps with a nilpotent one

Degree $2$ nilpotent matrices with non-zero product and subset products not depending on the order

nilpotent algebraic groups in terms of extensions

Matrix representations and idempotent/nilpotent elements

On a question about nilpotent matrices

Why are eigenvalues of nilpotent matrices equal to zero?

Finding a non-zero vector in both the column space and the null space of a nilpotent matrix

Prove that $ \text{rank}(A^{3}) < \text{rank}(A^{2}) < \text{rank}(A) $ if $ A $ is a $ (10 \times 10) $-matrix with nilpotence equal to $ 3 $.

Carter Subgroups and Projectors

Nilpotent matrices: is there a fast trick to find the degree?

Find endomorphisms $α$ and $β$ of $V$ satisfying the condition that $αβ$ is not nilpotent but $cα+dβ$ is nilpotent for all $c, d ∈ \mathbb{R}$

Let $V$ be a vector space and $\alpha$ a nilpotent endomorfism (of degree $k$), how can I show that $\alpha(x)+x$ is epic?

Let $\dim(V)<\infty$ . Do there exist endomorphisms of $V$ satisfying the condition that $σ_1 + αβ − βα$ is nilpotent?

The number of $3\times 3$ nilpotent matrices over $\mathbb{F}_q$ using the orbit-stabilizer theorem

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