Question

Let $A\in M_n(\Bbb{C})$, show that the followings are equivalent.

score 77 · Answer 1 · 2018-10-06 14:21:06

77

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Let $A\in M_n(\Bbb{C})$, show that the followings are equivalent.

Published on 06 Oct 2018 - 14:21

score 77 · Answer 2 · 2018-10-06 19:52:00

77

Views

Let $A\in M_n(\Bbb{C})$ such that $\text{Im}(A)\cap\text{Ker}(A)=\theta$

Published on 06 Oct 2018 - 19:52

score 53 · Answer 3 · 2018-10-07 10:15:14

53

Views

Solving Linear Systems - Criteria for Rank Condition

Published on 07 Oct 2018 - 10:15

score 436 · Answer 4 · 2018-10-07 14:04:35

436

Views

How to determine the eigen values of $A^tA$ where $x^tA A^tx=\alpha x^tx ~~~~ \forall x \in \Bbb{R}^m$ holds for some $\alpha$

Published on 07 Oct 2018 - 14:04

score 46 · Answer 5 · 2018-10-09 08:52:45

46

Views

What's the rank of $\sum_{i=1}^{m}x_{i}y_{i}^{T} \leq m$?

Published on 09 Oct 2018 - 8:52

score 101 · Answer 6 · 2018-10-10 07:13:12

101

Views

Find rank of the special block symmetric and persymmetric matrix

Published on 10 Oct 2018 - 7:13

score 49 · Answer 7 · 2018-10-10 16:28:44

49

Views

Significance of column vectors of a matrix

Published on 10 Oct 2018 - 16:28

score 120 · Answer 8 · 2018-10-11 04:03:18

120

Views

Prove rank($A$)=rank($B$) if $A+B=AB,\ and\ A,B \in M_n(F)$.

Published on 11 Oct 2018 - 4:03

score 46 · Answer 9 · 2018-10-12 08:32:39

46

Views

Show a matrix with a specific sign pattern has full rank.

Published on 12 Oct 2018 - 8:32

score 76 · Answer 10 · 2018-10-12 16:44:46

76

Views

Show that an algebraic variety is not irreducible.

Published on 12 Oct 2018 - 16:44

score 34 · Answer 11 · 2018-10-17 14:06:15

34

Views

For which $x\in\mathbb{R}$ does the vector system rank third

Published on 17 Oct 2018 - 14:06

score 70 · Answer 12 · 2026-03-25 18:48:06

70

Views

Distinguishing between two possibilities for the Jordan normal form of a matrix

Published on 25 Mar 2026 - 18:48

score 182 · Answer 13 · 2018-10-21 18:09:11

182

Views

Why is the adjugate matrix the null matrix?

Published on 21 Oct 2018 - 18:09

score 291 · Answer 14 · 2018-10-21 20:02:05

291

Views

How to calculate the rank of matrix with vertical and horizontal line

Published on 21 Oct 2018 - 20:02

score 406 · Answer 15 · 2018-10-21 22:08:38

406

Views

If rank$(A) = 2$, then $A^2 \neq 0_3$

Published on 21 Oct 2018 - 22:08

List Question

Let $A\in M_n(\Bbb{C})$, show that the followings are equivalent.

Let $A\in M_n(\Bbb{C})$ such that $\text{Im}(A)\cap\text{Ker}(A)=\theta$

Solving Linear Systems - Criteria for Rank Condition

How to determine the eigen values of $A^tA$ where $x^tA A^tx=\alpha x^tx ~~~~ \forall x \in \Bbb{R}^m$ holds for some $\alpha$

What's the rank of $\sum_{i=1}^{m}x_{i}y_{i}^{T} \leq m$?

Find rank of the special block symmetric and persymmetric matrix

Significance of column vectors of a matrix

Prove rank($A$)=rank($B$) if $A+B=AB,\ and\ A,B \in M_n(F)$.

Show a matrix with a specific sign pattern has full rank.

Show that an algebraic variety is not irreducible.

For which $x\in\mathbb{R}$ does the vector system rank third

Distinguishing between two possibilities for the Jordan normal form of a matrix

Why is the adjugate matrix the null matrix?

How to calculate the rank of matrix with vertical and horizontal line

If rank$(A) = 2$, then $A^2 \neq 0_3$

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