Question

How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

score 130.6k · Answer 1 · 2011-07-02 07:03:41

130.6k

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How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

Published on 02 Jul 2011 - 7:03

score 19.1k · Answer 2 · 2011-08-24 14:18:33

19.1k

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Show that $\operatorname{rank}(A+B) \leq \operatorname{rank}(A) + \operatorname{rank}(B)$

Published on 24 Aug 2011 - 14:18

score 32.7k · Answer 3 · 2011-10-31 22:27:27

32.7k

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Is the rank of $AB$ always equal to the rank of $BA$?

Published on 31 Oct 2011 - 22:27

score 628 · Answer 4 · 2026-03-26 04:30:13

628

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Parallel rank computation of huge sparse matrices over the binary field

Published on 26 Mar 2026 - 4:30

score 1.2k · Answer 5 · 2012-01-20 13:49:08

1.2k

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Minimize $ \|A-BXC \|_F$ subject to $\mbox{rank} (X) \leq r$

Published on 20 Jan 2012 - 13:49

score 62.6k · Answer 6 · 2026-03-27 17:57:33

62.6k

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Proving: "The trace of an idempotent matrix equals the rank of the matrix"

Published on 27 Mar 2026 - 17:57

score 466 · Answer 7 · 2026-03-28 08:09:24

466

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How would changing of elements of matrix(from zeros to non-zeros) affect its rank.

Published on 28 Mar 2026 - 8:09

score 6.5k · Answer 8 · 2012-06-16 22:03:23

6.5k

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Relationship: Rank of a matrix $\leftrightarrow$ # of eigenvalues

Published on 16 Jun 2012 - 22:03

score 24.9k · Answer 9 · 2026-03-25 11:14:53

24.9k

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Why is minimizing the nuclear norm of a matrix a good surrogate for minimizing the rank?

Published on 25 Mar 2026 - 11:14

score 11.4k · Answer 10 · 2012-08-27 14:58:11

11.4k

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Proof that determinant rank equals row/column rank

Published on 27 Aug 2012 - 14:58

score 69k · Answer 11 · 2012-09-07 01:25:53

69k

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Rank product of matrix compared to individual matrices.

Published on 07 Sep 2012 - 1:25

score 2.6k · Answer 12 · 2012-11-29 00:50:55

2.6k

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Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$

Published on 29 Nov 2012 - 0:50

score 1.2k · Answer 13 · 2012-12-01 12:46:17

1.2k

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Show that $rank(A)+rank(B) \leq n$, when $A,B$ are $2$ matrices of size $n \times n$, and $AB=0$

Published on 01 Dec 2012 - 12:46

score 14.3k · Answer 14 · 2013-01-02 23:54:51

14.3k

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Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$

Published on 02 Jan 2013 - 23:54

score 1.6k · Answer 15 · 2013-01-05 09:23:26

1.6k

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Why is a full-rank matrix in a finite field also full-rank in an expanded finite field?

Published on 05 Jan 2013 - 9:23

List Question

How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?

Show that $\operatorname{rank}(A+B) \leq \operatorname{rank}(A) + \operatorname{rank}(B)$

Is the rank of $AB$ always equal to the rank of $BA$?

Parallel rank computation of huge sparse matrices over the binary field

Minimize $ \|A-BXC \|_F$ subject to $\mbox{rank} (X) \leq r$

Proving: "The trace of an idempotent matrix equals the rank of the matrix"

How would changing of elements of matrix(from zeros to non-zeros) affect its rank.

Relationship: Rank of a matrix $\leftrightarrow$ # of eigenvalues

Why is minimizing the nuclear norm of a matrix a good surrogate for minimizing the rank?

Proof that determinant rank equals row/column rank

Rank product of matrix compared to individual matrices.

Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$

Show that $rank(A)+rank(B) \leq n$, when $A,B$ are $2$ matrices of size $n \times n$, and $AB=0$

Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$

Why is a full-rank matrix in a finite field also full-rank in an expanded finite field?

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