Question

(idempotent)Does $rank(A) + rank(A-I_n)=n$ implies $A^2=A$?

score 24 · Answer 1 · 2026-03-26 09:19:47

24

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(idempotent)Does $rank(A) + rank(A-I_n)=n$ implies $A^2=A$?

Published on 26 Mar 2026 - 9:19

score 212 · Answer 2 · 2023-06-04 18:32:15

212

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$V=\left \{ C|\space C\in M_{q\times r}(R)\space such \space that\space ACB=O \right \} $, find the dimension of the vector space V

Published on 04 Jun 2023 - 18:32

score 240 · Answer 3 · 2023-06-06 09:41:32

240

Views

If the $m \times n$ linear system $Ax = b$ has a unique solution then $r = n$.

Published on 06 Jun 2023 - 9:41

score 111 · Answer 4 · 2023-06-06 13:41:44

111

Views

Let $A_{m\times n},B_{n\times m}$, prove $\text{rank}(A)=\text{rank}(B)=m\implies \text{rank}(BA)=m$

Published on 06 Jun 2023 - 13:41

score 74 · Answer 5 · 2026-03-27 22:00:29

74

Views

Low rank approximation with MSE approach

Published on 27 Mar 2026 - 22:00

score 84 · Answer 6 · 2026-03-25 05:10:03

84

Views

Rank of a square matrix is equal to the size of the largest invertible submatrix

Published on 25 Mar 2026 - 5:10

score 48 · Answer 7 · 2026-03-25 19:03:56

48

Views

Permutation of a rank-$r$ matrix

Published on 25 Mar 2026 - 19:03

score 45 · Answer 8 · 2026-03-26 23:59:50

45

Views

Reference request for this classic result about block matrices

Published on 26 Mar 2026 - 23:59

score 274 · Answer 9 · 2026-03-25 09:47:15

274

Views

How to approximate a rank-1 solution after exploiting semidefinite relaxation method?

Published on 25 Mar 2026 - 9:47

score 113 · Answer 10 · 2026-02-23 07:00:20

113

Views

Prove that there is a rank one matrix $B$ so that $Bx = y$ where $B$ has matrix norm $1$

Published on 23 Feb 2026 - 7:00

score 66 · Answer 11 · 2023-06-17 08:59:33

66

Views

Minimum value of $\operatorname{rank} (A+B)$

Published on 17 Jun 2023 - 8:59

score 182 · Answer 12 · 2023-06-19 14:33:38

182

Views

Rank of a matrix with $a_{ii}=0$ and $a_{ij}+a_{ji}=1$

Published on 19 Jun 2023 - 14:33

score 31 · Answer 13 · 2023-06-26 10:22:46

31

Views

rank of partitioned matrix with column space information

Published on 26 Jun 2023 - 10:22

score 36 · Answer 14 · 2023-07-03 10:35:49

36

Views

I can't find the nth power of a matrix

Published on 03 Jul 2023 - 10:35

score 13 · Answer 15 · 2026-03-01 00:09:50

13

Views

Is the Schmidt rank finite for finite ranked operators in infinite dimensional Hilbert spaces

Published on 01 Mar 2026 - 0:09

List Question

(idempotent)Does $rank(A) + rank(A-I_n)=n$ implies $A^2=A$?

$V=\left \{ C|\space C\in M_{q\times r}(R)\space such \space that\space ACB=O \right \} $, find the dimension of the vector space V

If the $m \times n$ linear system $Ax = b$ has a unique solution then $r = n$.

Let $A_{m\times n},B_{n\times m}$, prove $\text{rank}(A)=\text{rank}(B)=m\implies \text{rank}(BA)=m$

Low rank approximation with MSE approach

Rank of a square matrix is equal to the size of the largest invertible submatrix

Permutation of a rank-$r$ matrix

Reference request for this classic result about block matrices

How to approximate a rank-1 solution after exploiting semidefinite relaxation method?

Prove that there is a rank one matrix $B$ so that $Bx = y$ where $B$ has matrix norm $1$

Minimum value of $\operatorname{rank} (A+B)$

Rank of a matrix with $a_{ii}=0$ and $a_{ij}+a_{ji}=1$

rank of partitioned matrix with column space information

I can't find the nth power of a matrix

Is the Schmidt rank finite for finite ranked operators in infinite dimensional Hilbert spaces

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