Question

Prove that row rank of a matrix equals column rank

score 5.1k · Answer 1 · 2014-09-21 06:12:12

5.1k

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Prove that row rank of a matrix equals column rank

Published on 21 Sep 2014 - 6:12

score 1.3k · Answer 2 · 2014-09-23 16:46:37

1.3k

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How to prove a property of ranks: $\operatorname{rank}(AB)= \operatorname{rank}(B)- \dim(\operatorname{Im} B \cap \ker A)$

Published on 23 Sep 2014 - 16:46

score 2k · Answer 3 · 2014-09-24 19:31:34

2k

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The rank after adding a rank-one matrix to a full rank matrix

Published on 24 Sep 2014 - 19:31

score 4.5k · Answer 4 · 2026-03-26 20:34:39

4.5k

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Expressing a rank-$k$ matrix as a sum of $k$ rank-$1$ matrices

Published on 26 Mar 2026 - 20:34

score 602 · Answer 5 · 2014-10-02 07:34:38

602

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Bordered minor and rank of a matrix

Published on 02 Oct 2014 - 7:34

score 224 · Answer 6 · 2014-10-06 19:29:02

224

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Is diagonal of sum matrix of rank one matrix and circulant matrix.

Published on 06 Oct 2014 - 19:29

score 4.8k · Answer 7 · 2014-10-07 16:05:03

4.8k

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Rank of a linear operator

Published on 07 Oct 2014 - 16:05

score 799 · Answer 8 · 2014-10-08 17:00:04

799

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"Degrees of freedom" of some low-rank skew-symmetric matrices

Published on 08 Oct 2014 - 17:00

score 2.4k · Answer 9 · 2014-10-08 22:34:15

2.4k

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If $A$ is an $m\times n$ matrix and $B$ is an $n\times m$ matrix such that $AB=I$, prove that rank$(B)=m$

Published on 08 Oct 2014 - 22:34

score 7k · Answer 10 · 2026-03-27 10:04:58

7k

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What properties does a rank-$1$ matrix have?

Published on 27 Mar 2026 - 10:04

score 559 · Answer 11 · 2014-10-11 20:55:45

559

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Show that the system is controllable (i.e. prove P has full rank)

Published on 11 Oct 2014 - 20:55

score 642 · Answer 12 · 2014-10-19 14:00:09

642

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Proving a theorem about trace of matrix which involving generalized inverse matrix

Published on 19 Oct 2014 - 14:00

score 10.2k · Answer 13 · 2014-10-22 09:25:54

10.2k

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Rank of a matrix and dimension of the image

Published on 22 Oct 2014 - 9:25

score 20.9k · Answer 14 · 2026-03-26 18:49:58

20.9k

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Relation between trace and rank for projection matrices

Published on 26 Mar 2026 - 18:49

score 50 · Answer 15 · 2014-10-23 19:23:39

50

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Find $x$ for which the rank is as minimal/maximal as possible

Published on 23 Oct 2014 - 19:23

List Question

Prove that row rank of a matrix equals column rank

How to prove a property of ranks: $\operatorname{rank}(AB)= \operatorname{rank}(B)- \dim(\operatorname{Im} B \cap \ker A)$

The rank after adding a rank-one matrix to a full rank matrix

Expressing a rank-$k$ matrix as a sum of $k$ rank-$1$ matrices

Bordered minor and rank of a matrix

Is diagonal of sum matrix of rank one matrix and circulant matrix.

Rank of a linear operator

"Degrees of freedom" of some low-rank skew-symmetric matrices

If $A$ is an $m\times n$ matrix and $B$ is an $n\times m$ matrix such that $AB=I$, prove that rank$(B)=m$

What properties does a rank-$1$ matrix have?

Show that the system is controllable (i.e. prove P has full rank)

Proving a theorem about trace of matrix which involving generalized inverse matrix

Rank of a matrix and dimension of the image

Relation between trace and rank for projection matrices

Find $x$ for which the rank is as minimal/maximal as possible

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