Question

Rank of matrix $AB$ when $A$ and $B$ have full rank

score 28k · Answer 1 · 2013-01-07 10:25:53

28k

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Rank of matrix $AB$ when $A$ and $B$ have full rank

Published on 07 Jan 2013 - 10:25

score 422 · Answer 2 · 2013-01-09 09:27:07

422

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Echelon form of matrix have the same rank, after operations modulo

Published on 09 Jan 2013 - 9:27

score 4.9k · Answer 3 · 2013-02-04 05:18:41

4.9k

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Vandermonde matrix rank

Published on 04 Feb 2013 - 5:18

score 1.6k · Answer 4 · 2026-03-28 14:56:53

1.6k

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The rank of a block matrix as a function of the rank of its submatrices.

Published on 28 Mar 2026 - 14:56

score 43.8k · Answer 5 · 2013-02-09 17:07:50

43.8k

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Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$

Published on 09 Feb 2013 - 17:07

score 6.4k · Answer 6 · 2026-03-29 05:34:11

6.4k

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Expected rank of a random binary matrix?

Published on 29 Mar 2026 - 5:34

score 10.4k · Answer 7 · 2026-03-28 14:56:49

10.4k

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Prove that the rank of a block diagonal matrix equals the sum of the ranks of the matrices that are the main diagonal blocks.

Published on 28 Mar 2026 - 14:56

score 70.9k · Answer 8 · 2013-03-17 16:20:53

70.9k

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Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix

Published on 17 Mar 2013 - 16:20

score 132 · Answer 9 · 2020-08-02 03:31:42

132

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What is the upper bound of $\operatorname{rank}(\lambda B - BA)$?

Published on 02 Aug 2020 - 3:31

score 259 · Answer 10 · 2020-08-02 19:33:09

Let $A$ be a square matrix and $A=BC$ be its rank factorization. Show that rank $(A)$=rank $(A^2)$ if and only if $CB$ is non-singular.

score 489 · Answer 11 · 2020-08-05 15:43:52

489

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Lower bound on the rank of a 0-1 matrix: $\mathrm {rank}_\mathbb R(A)\cdot |A|\geq n^2$

Published on 05 Aug 2020 - 15:43

score 623 · Answer 12 · 2020-08-07 14:03:43

623

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Show $A$ is diagonalizable if $1$ is an eigenvalue and $A$ has non-zero rank.

Published on 07 Aug 2020 - 14:03

score 76 · Answer 13 · 2026-04-02 11:25:39

76

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About rank of matrix

Published on 02 Apr 2026 - 11:25

score 508 · Answer 14 · 2020-08-10 15:10:21

508

Views

Solution for least squares problem

Published on 10 Aug 2020 - 15:10

score 40 · Answer 15 · 2020-08-12 04:33:41

40

Views

How to judge the rank relationship of matrix equation $AB=E$

Published on 12 Aug 2020 - 4:33

List Question

Rank of matrix $AB$ when $A$ and $B$ have full rank

Echelon form of matrix have the same rank, after operations modulo

Vandermonde matrix rank

The rank of a block matrix as a function of the rank of its submatrices.

Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$

Expected rank of a random binary matrix?

Prove that the rank of a block diagonal matrix equals the sum of the ranks of the matrices that are the main diagonal blocks.

Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix

What is the upper bound of $\operatorname{rank}(\lambda B - BA)$?

Let $A$ be a square matrix and $A=BC$ be its rank factorization. Show that rank $(A)$=rank $(A^2)$ if and only if $CB$ is non-singular.

Lower bound on the rank of a 0-1 matrix: $\mathrm {rank}_\mathbb R(A)\cdot |A|\geq n^2$

Show $A$ is diagonalizable if $1$ is an eigenvalue and $A$ has non-zero rank.

About rank of matrix

Solution for least squares problem

How to judge the rank relationship of matrix equation $AB=E$

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