List questions from matrix-rank

Published on 29 Jun 2014 - 20:05

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Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$

Published on 01 Jul 2014 - 14:13

2.7k

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Rank of transformation $Y=AX-XA$

Published on 07 Jul 2014 - 10:51

1.5k

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A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.

Published on 09 Jul 2014 - 0:28

409

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$A+A^2B+B=0$ implies $A^2+I$ invertible?

Published on 09 Jul 2014 - 13:45

265

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Cross-product is a left singular vector?

Published on 26 Mar 2026 - 9:16

1.6k

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Equality case in the Frobenius rank inequality

Published on 20 Jul 2014 - 13:35

93

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$A$ is an $m\times n$ matrix and $B$ is an $n\times p$ matrix, show that $\text{rank}(AB)\le\text{rank}(A)$.

Published on 24 Jul 2014 - 5:41

100

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What is the minimum number of sign patterns in $\frac n2$ of columns (or rows) of Hadamard matrices?

Published on 25 Mar 2026 - 6:06

51

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Help for proving rank of matrix

Published on 25 Jul 2014 - 5:37

39.6k

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Rank of a Matrix Sum

Published on 25 Jul 2014 - 11:37

83

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Matrix Rank calculation

Published on 25 Jul 2014 - 12:04

56

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Rank of a simple matrix series

Published on 25 Jul 2014 - 12:29

1k

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How to find the rank of a Toeplitz matrix?

Published on 25 Mar 2026 - 2:00

304

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$\text{rank}(AB^2)=\text{rank}(AB)$

Published on 03 Aug 2014 - 6:22

List Question

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

Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$

Rank of transformation $Y=AX-XA$

A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.

$A+A^2B+B=0$ implies $A^2+I$ invertible?

Cross-product is a left singular vector?

Equality case in the Frobenius rank inequality

$A$ is an $m\times n$ matrix and $B$ is an $n\times p$ matrix, show that $\text{rank}(AB)\le\text{rank}(A)$.

What is the minimum number of sign patterns in $\frac n2$ of columns (or rows) of Hadamard matrices?

Help for proving rank of matrix

Rank of a Matrix Sum

Matrix Rank calculation

Rank of a simple matrix series

How to find the rank of a Toeplitz matrix?

$\text{rank}(AB^2)=\text{rank}(AB)$

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