List questions from matrix-rank

Published on 30 Sep 2016 - 20:43

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A square matrix $A$ is such that $\mathrm{rank}(A^{k}) = \mathrm{rank}(A^{k+1})$

Published on 01 Oct 2016 - 17:20

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Rank of matrix with variable

Published on 26 Mar 2026 - 23:50

396

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How to write $ uv^{\top} + vu^{\top} $ as $ xx^{\top} + yy^{\top} $?

Published on 05 Oct 2016 - 16:50

603

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Let $A$ and $B$ be two square Hermitian matrices such that $AB = 0 = BA$. Prove that $\mbox{rank} (A + B) = \mbox{rank}(A) + \mbox{rank} (B)$.

Published on 06 Oct 2016 - 16:15

78

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What can be the rank of the following matrix, where $a$ is a parameter?

Published on 11 Oct 2016 - 19:22

1.2k

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Power iteration with rank-$1$ matrix

Published on 13 Oct 2016 - 7:17

79

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A and B are 3x3 matrices. Show that $AB \neq 0$ if both matrices have a rank of 2.

Published on 16 Oct 2016 - 6:40

846

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Rank + nullity theorem

Published on 16 Oct 2016 - 12:58

186

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Proof that $A$ is diagonalizable iff rank$(A-tI)=$rank$((A-tI)^2)$ for all $t\in\mathbb C$.

Published on 16 Oct 2016 - 15:21

4.4k

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If $\operatorname{rank}(A)$ = $\operatorname{rank}(A^2)$, show that nullspace of $A$ = nullspace of $A^2$

Published on 17 Oct 2016 - 2:04

288

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Rank of matrices composed of identity matrices

Published on 20 Oct 2016 - 13:41

1.2k

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Basis for a column space of a matrix

Published on 21 Oct 2016 - 18:54

1.2k

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Prove matrix $uu^T+vv^T$ has rank two.

Published on 23 Oct 2016 - 6:46

207

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matrix with variable and their rank

Published on 24 Oct 2016 - 7:00

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Similar Matrices in a field

A square matrix $A$ is such that $\mathrm{rank}(A^{k}) = \mathrm{rank}(A^{k+1})$

Rank of matrix with variable

How to write $ uv^{\top} + vu^{\top} $ as $ xx^{\top} + yy^{\top} $?

Let $A$ and $B$ be two square Hermitian matrices such that $AB = 0 = BA$. Prove that $\mbox{rank} (A + B) = \mbox{rank}(A) + \mbox{rank} (B)$.

What can be the rank of the following matrix, where $a$ is a parameter?

Power iteration with rank-$1$ matrix

A and B are 3x3 matrices. Show that $AB \neq 0$ if both matrices have a rank of 2.

Rank + nullity theorem

Proof that $A$ is diagonalizable iff rank$(A-tI)=$rank$((A-tI)^2)$ for all $t\in\mathbb C$.

If $\operatorname{rank}(A)$ = $\operatorname{rank}(A^2)$, show that nullspace of $A$ = nullspace of $A^2$

Rank of matrices composed of identity matrices

Basis for a column space of a matrix

Prove matrix $uu^T+vv^T$ has rank two.

matrix with variable and their rank

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