Question

$A, B $ be $n \times n$ real matrices such that $A$ is singular and $B$ is non-singular, then prove or disprove $\text{Rank}(AB)=\text{Rank}(A)$

score 352 · Answer 1 · 2019-07-30 06:35:04

352

Views

$A, B $ be $n \times n$ real matrices such that $A$ is singular and $B$ is non-singular, then prove or disprove $\text{Rank}(AB)=\text{Rank}(A)$

Published on 30 Jul 2019 - 6:35

score 6.2k · Answer 2 · 2019-07-31 01:50:00

6.2k

Views

Can I exchange column and then use the row transformation when converting a matrix into a row echelon form?

Published on 31 Jul 2019 - 1:50

score 93 · Answer 3 · 2019-07-31 16:36:19

93

Views

How do we compare the nullity of an adjacency matrix and an incidence matrix of a simple graph?

Published on 31 Jul 2019 - 16:36

score 43 · Answer 4 · 2019-08-01 16:55:35

43

Views

System of equations has has no solution if $q > 0$, then what is the value of $q$?

Published on 01 Aug 2019 - 16:55

score 198 · Answer 5 · 2019-08-03 03:02:27

198

Views

Given two matrices A and B, what is the rank of AB?

Published on 03 Aug 2019 - 3:02

score 52 · Answer 6 · 2026-03-25 05:06:43

52

Views

Relation between condition number of two related matrices

Published on 25 Mar 2026 - 5:06

score 34 · Answer 7 · 2019-08-07 01:15:32

34

Views

Is the block Hankel Matrix low rank if its associated 1D Hankel matrix are low rank?

Published on 07 Aug 2019 - 1:15

score 493 · Answer 8 · 2019-08-08 20:39:52

493

Views

Derivative of determinant is zero iff co-rank is at least two?

Published on 08 Aug 2019 - 20:39

score 70 · Answer 9 · 2019-08-11 09:37:18

70

Views

A problem on rank of real or complex matrices .

Published on 11 Aug 2019 - 9:37

score 50 · Answer 10 · 2019-08-11 15:26:31

50

Views

The inverse in the sense of MOORE-PENROSAE $AA^{-1}B=B$

Published on 11 Aug 2019 - 15:26

score 658 · Answer 11 · 2026-03-26 13:02:22

658

Views

Proof rank linear map is equal to the rank of its transformation matrix

Published on 26 Mar 2026 - 13:02

score 137 · Answer 12 · 2019-08-14 08:06:40

137

Views

What is the complexity order of Kalman rank condition?

Published on 14 Aug 2019 - 8:06

score 184 · Answer 13 · 2019-08-15 21:40:41

184

Views

Show that $\mathrm{rank}(A)=n$ iff $\mathrm{rref} A$ has no zero columns.

Published on 15 Aug 2019 - 21:40

score 68 · Answer 14 · 2019-08-17 13:18:46

68

Views

Linearly dependent matrix columns implies zeroes in the solution of the system of equation given by this matrix?

Published on 17 Aug 2019 - 13:18

score 69 · Answer 15 · 2019-08-18 11:19:28

69

Views

Understand the rank of $ \begin{bmatrix} A&b\\ b^{*}&0 \end{bmatrix}$

Published on 18 Aug 2019 - 11:19

List Question

$A, B $ be $n \times n$ real matrices such that $A$ is singular and $B$ is non-singular, then prove or disprove $\text{Rank}(AB)=\text{Rank}(A)$

Can I exchange column and then use the row transformation when converting a matrix into a row echelon form?

How do we compare the nullity of an adjacency matrix and an incidence matrix of a simple graph?

System of equations has has no solution if $q > 0$, then what is the value of $q$?

Given two matrices A and B, what is the rank of AB?

Relation between condition number of two related matrices

Is the block Hankel Matrix low rank if its associated 1D Hankel matrix are low rank?

Derivative of determinant is zero iff co-rank is at least two?

A problem on rank of real or complex matrices .

The inverse in the sense of MOORE-PENROSAE $AA^{-1}B=B$

Proof rank linear map is equal to the rank of its transformation matrix

What is the complexity order of Kalman rank condition?

Show that $\mathrm{rank}(A)=n$ iff $\mathrm{rref} A$ has no zero columns.

Linearly dependent matrix columns implies zeroes in the solution of the system of equation given by this matrix?

Understand the rank of $ \begin{bmatrix} A&b\\ b^{*}&0 \end{bmatrix}$

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