List questions from matrix-rank

Published on 25 Mar 2026 - 6:00

203

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Rank is less than $\frac n2$

Published on 25 Mar 2026 - 9:48

1.6k

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If $A$ is a symmetric matrix, then rank($A^{n}$) = rank($A$). Is, this statement true?

Published on 30 Jul 2018 - 9:03

102

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Linear algebra question with rank-1 matrices

Published on 30 Jul 2018 - 21:21

72

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System of equations involving rank-1 matrices

Published on 31 Jul 2018 - 21:07

302

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Rank-Deficiency in an Augmented Matrix comprised of Two Full Rank Matrices

Published on 01 Aug 2018 - 2:17

555

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Inconsistent solutions and their image/kernel

Published on 03 Aug 2018 - 14:28

1.3k

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rank and orthogonal projection

Published on 03 Aug 2018 - 14:34

1k

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Rank of a matrix related to consistency

Published on 04 Aug 2018 - 16:15

69

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Can we stay invertible while approximating linear maps in Sobolev spaces?

Published on 25 Mar 2026 - 5:06

9.8k

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Does $\operatorname{rank} (A^2) = \operatorname{rank} (A)$ for any matrix $A\in \operatorname{Mat}_{n \times n}$?

Published on 05 Aug 2018 - 15:12

80

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Find a pair $(A,B)\in M_n(\mathbb C)^2$ such that the rank of $AB-BA-I_n$ is $1$

Published on 07 Aug 2018 - 0:27

508

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Rank-$1$ matrices and the inequality $\operatorname{rank} (A+B) \leq \operatorname{rank} (A) + \operatorname{rank} (B)$

Published on 25 Mar 2026 - 3:22

100

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Matrix , rank of a matrix

Published on 09 Aug 2018 - 18:50

315

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If $C$ is nonsingular, show that $A$ and $C^TAC$ have the same rank.

Published on 11 Aug 2018 - 13:48

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Regular maps: What is it, what does it, who names it

Rank is less than $\frac n2$

If $A$ is a symmetric matrix, then rank($A^{n}$) = rank($A$). Is, this statement true?

Linear algebra question with rank-1 matrices

System of equations involving rank-1 matrices

Rank-Deficiency in an Augmented Matrix comprised of Two Full Rank Matrices

Inconsistent solutions and their image/kernel

rank and orthogonal projection

Rank of a matrix related to consistency

Can we stay invertible while approximating linear maps in Sobolev spaces?

Does $\operatorname{rank} (A^2) = \operatorname{rank} (A)$ for any matrix $A\in \operatorname{Mat}_{n \times n}$?

Find a pair $(A,B)\in M_n(\mathbb C)^2$ such that the rank of $AB-BA-I_n$ is $1$

Rank-$1$ matrices and the inequality $\operatorname{rank} (A+B) \leq \operatorname{rank} (A) + \operatorname{rank} (B)$

Matrix , rank of a matrix

If $C$ is nonsingular, show that $A$ and $C^TAC$ have the same rank.

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