List questions from matrix-rank

Published on 28 Nov 2017 - 14:46

95

Views

matrix inversion with low-rank trace update

Published on 02 Apr 2026 - 1:21

4.1k

Views

Let $A$ be an $m\times n$ matrix. Prove that $\operatorname{rank}(AA^T) = \operatorname{rank}(A)$.

Published on 27 Mar 2026 - 13:02

28

Views

Proof about rank of a matrix depending on the value of its determinant

Published on 05 Dec 2017 - 17:09

306

Views

Rank of a matrix of L.T. which is not one one

Published on 06 Dec 2017 - 5:59

44

Views

How to show that $\operatorname{rank}(A) \le 4$ and $A + A^T$ is irreversible

Published on 06 Dec 2017 - 23:24

101

Views

problem about the dimensions of two subspaces

Published on 07 Dec 2017 - 1:36

890

Views

Let $A$ be a $10 \times 15$ non-zero matrix. What are the possible values of the rank of $A$ and the nullity of $A$?

Published on 11 Dec 2017 - 12:04

1.3k

Views

If $A \in \mathbb{M}_{n\times n}(\mathbb{R})$ with $n\ge 2$ has rank $1$

Published on 14 Dec 2017 - 14:52

602

Views

Show that if $c$ is a point of $\Bbb{R}^n$ sufficiently close to $0$, then the equation $f(x)=c$ has a solution.

Published on 14 Dec 2017 - 15:37

397

Views

What does adding between dimensions mean if anything at all? Are there useful conventions for doing so?

Published on 25 Mar 2026 - 17:45

85

Views

Complete the matrix through a rank-one approximation.

Published on 26 Mar 2026 - 1:27

5.9k

Views

$A^TA$ is non-singular if and only if $A$ has full row rank

Published on 14 Dec 2017 - 18:17

340

Views

Prove if $U$ is surjective, then $T$ is injective as $UT = 0$

Published on 15 Dec 2017 - 16:58

126

Views

how to show existence of such a matrix

Published on 16 Dec 2017 - 7:15

List Question

Simple matrix reasoning

matrix inversion with low-rank trace update

Let $A$ be an $m\times n$ matrix. Prove that $\operatorname{rank}(AA^T) = \operatorname{rank}(A)$.

Proof about rank of a matrix depending on the value of its determinant

Rank of a matrix of L.T. which is not one one

How to show that $\operatorname{rank}(A) \le 4$ and $A + A^T$ is irreversible

problem about the dimensions of two subspaces

Let $A$ be a $10 \times 15$ non-zero matrix. What are the possible values of the rank of $A$ and the nullity of $A$?

If $A \in \mathbb{M}_{n\times n}(\mathbb{R})$ with $n\ge 2$ has rank $1$

Show that if $c$ is a point of $\Bbb{R}^n$ sufficiently close to $0$, then the equation $f(x)=c$ has a solution.

What does adding between dimensions mean if anything at all? Are there useful conventions for doing so?

Complete the matrix through a rank-one approximation.

$A^TA$ is non-singular if and only if $A$ has full row rank

Prove if $U$ is surjective, then $T$ is injective as $UT = 0$

how to show existence of such a matrix

Trending Questions

Popular # Hahtags

Popular Questions