Question

Given $n \times n$ matrices, $A$ and $B$, show that ${\rm rank}(AB) \leq {\rm rank}(A)$

score 147 · Answer 1 · 2017-05-18 23:47:05

147

Views

Given $n \times n$ matrices, $A$ and $B$, show that ${\rm rank}(AB) \leq {\rm rank}(A)$

Published on 18 May 2017 - 23:47

score 42 · Answer 2 · 2017-05-19 21:17:45

42

Views

Finding the rank

Published on 19 May 2017 - 21:17

score 102 · Answer 3 · 2026-03-18 02:19:33

102

Views

Why is the following true? $\operatorname{rank}(A^G A) = \operatorname{rank}(A)$

Published on 18 Mar 2026 - 2:19

score 94 · Answer 4 · 2026-03-25 16:08:33

94

Views

Boston's "Spaces of constant rank matrices over $\mathrm{GF}(2)$"

Published on 25 Mar 2026 - 16:08

score 768 · Answer 5 · 2017-05-22 06:41:01

768

Views

A question on rank of powers of matrices

Published on 22 May 2017 - 6:41

score 72 · Answer 6 · 2017-05-23 13:37:16

72

Views

Counter-example Linear Algebra Question - Rank

Published on 23 May 2017 - 13:37

score 406 · Answer 7 · 2026-03-18 02:18:44

406

Views

Proof Involving Generalized Inverse Matrices and Rank

Published on 18 Mar 2026 - 2:18

score 443 · Answer 8 · 2017-05-26 20:01:34

443

Views

Matrices and eigenvalues

Published on 26 May 2017 - 20:01

score 585 · Answer 9 · 2026-03-25 20:36:03

585

Views

Rank of adjacency matrix of twin-free bipartite graph and maximum matching

Published on 25 Mar 2026 - 20:36

score 146 · Answer 10 · 2017-05-30 08:33:04

146

Views

the rank of a matrix that is combined by two

Published on 30 May 2017 - 8:33

score 4.3k · Answer 11 · 2017-05-31 02:46:37

4.3k

Views

Is it true any real matrix add an identity matrix is full rank?

Published on 31 May 2017 - 2:46

score 39 · Answer 12 · 2026-04-01 23:58:15

39

Views

Show that $\{A\in Hom(\Bbb R^n, \Bbb R^m ) | \mathrm{A \:has \:maximum \: Rank}\}$ is dense in $Hom(\Bbb R^n, \Bbb R^m )$

Published on 01 Apr 2026 - 23:58

score 129 · Answer 13 · 2026-03-18 02:18:44

129

Views

How can I compute eigenvalues or characteristic polynomial of this matrix? Please help.

Published on 18 Mar 2026 - 2:18

score 54 · Answer 14 · 2017-06-02 01:32:04

54

Views

I want to compute the eigenvalue of this matrix. Help me, please.

Published on 02 Jun 2017 - 1:32

score 875 · Answer 15 · 2026-03-29 08:35:36

875

Views

Prove that bilinear form can be presented as product of linear forms if and only if it has rank one

Published on 29 Mar 2026 - 8:35

List Question

Given $n \times n$ matrices, $A$ and $B$, show that ${\rm rank}(AB) \leq {\rm rank}(A)$

Finding the rank

Why is the following true? $\operatorname{rank}(A^G A) = \operatorname{rank}(A)$

Boston's "Spaces of constant rank matrices over $\mathrm{GF}(2)$"

A question on rank of powers of matrices

Counter-example Linear Algebra Question - Rank

Proof Involving Generalized Inverse Matrices and Rank

Matrices and eigenvalues

Rank of adjacency matrix of twin-free bipartite graph and maximum matching

the rank of a matrix that is combined by two

Is it true any real matrix add an identity matrix is full rank?

Show that $\{A\in Hom(\Bbb R^n, \Bbb R^m ) | \mathrm{A \:has \:maximum \: Rank}\}$ is dense in $Hom(\Bbb R^n, \Bbb R^m )$

How can I compute eigenvalues or characteristic polynomial of this matrix? Please help.

I want to compute the eigenvalue of this matrix. Help me, please.

Prove that bilinear form can be presented as product of linear forms if and only if it has rank one

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