Question

Prove $\operatorname{rank }(A) \le 4$ if $Ax_1=\cdots=Ax_7$ and $x_i$s are linearly independent

score 110 · Answer 1 · 2019-02-01 16:40:24

110

Views

Prove $\operatorname{rank }(A) \le 4$ if $Ax_1=\cdots=Ax_7$ and $x_i$s are linearly independent

Published on 01 Feb 2019 - 16:40

score 492 · Answer 2 · 2026-03-25 17:42:19

492

Views

What is the expectation of the rank of a matrix with a 1 at each column?

Published on 25 Mar 2026 - 17:42

score 42 · Answer 3 · 2019-02-03 12:21:09

42

Views

Rank, invertibility and solution spaces

Published on 03 Feb 2019 - 12:21

score 176 · Answer 4 · 2019-02-04 16:37:56

176

Views

Rank/determinant of the $n\times n$ matrix $((a_{ij}))$ where $a_{ij}=(i+j-1)^2$

Published on 04 Feb 2019 - 16:37

score 28 · Answer 5 · 2019-02-05 13:47:13

28

Views

Trouble moving forward in the proof of Rank Nullity theorem

Published on 05 Feb 2019 - 13:47

score 507 · Answer 6 · 2019-02-05 18:03:24

507

Views

Deleting any column from this matrix doesn't change the rank?

Published on 05 Feb 2019 - 18:03

score 36 · Answer 7 · 2019-02-06 15:18:22

36

Views

Determining the rank of a matrix, am I missing something?

Published on 06 Feb 2019 - 15:18

score 78 · Answer 8 · 2026-02-23 06:26:32

78

Views

How far from a matrix the rank does not decrease?

Published on 23 Feb 2026 - 6:26

score 22 · Answer 9 · 2026-03-25 12:52:07

22

Views

What is the angle between a $A_{3x3}$ with $Rank(A)=2$ and $A^T$

Published on 25 Mar 2026 - 12:52

score 135 · Answer 10 · 2026-03-25 11:03:23

135

Views

Connection between ranks of an endomorphism and its linear image on the exterior power

Published on 25 Mar 2026 - 11:03

score 358 · Answer 11 · 2019-02-11 13:12:31

358

Views

Rouché-Capelli theorem

Published on 11 Feb 2019 - 13:12

score 1.6k · Answer 12 · 2019-02-12 02:04:59

1.6k

Views

Is it possible to have Ran A = Ker $A^{T}$

Published on 12 Feb 2019 - 2:04

score 58 · Answer 13 · 2019-02-15 21:33:31

58

Views

Minimum number of non-zero entry in each row and column such that a matrix has maximum rank

Published on 15 Feb 2019 - 21:33

score 257 · Answer 14 · 2026-03-25 19:04:57

257

Views

Can $A + uv^T$ be non-singular if A(order n) has rank n-1

Published on 25 Mar 2026 - 19:04

score 70 · Answer 15 · 2026-03-25 09:39:42

70

Views

Can we perturb a low rank map to a full rank map in a smooth way?

Published on 25 Mar 2026 - 9:39

List Question

Prove $\operatorname{rank }(A) \le 4$ if $Ax_1=\cdots=Ax_7$ and $x_i$s are linearly independent

What is the expectation of the rank of a matrix with a 1 at each column?

Rank, invertibility and solution spaces

Rank/determinant of the $n\times n$ matrix $((a_{ij}))$ where $a_{ij}=(i+j-1)^2$

Trouble moving forward in the proof of Rank Nullity theorem

Deleting any column from this matrix doesn't change the rank?

Determining the rank of a matrix, am I missing something?

How far from a matrix the rank does not decrease?

What is the angle between a $A_{3x3}$ with $Rank(A)=2$ and $A^T$

Connection between ranks of an endomorphism and its linear image on the exterior power

Rouché-Capelli theorem

Is it possible to have Ran A = Ker $A^{T}$

Minimum number of non-zero entry in each row and column such that a matrix has maximum rank

Can $A + uv^T$ be non-singular if A(order n) has rank n-1

Can we perturb a low rank map to a full rank map in a smooth way?

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