Question

Why is rank $uv^{T}$ always equal to 1?

score 7.3k · Answer 1 · 2016-10-24 09:33:35

7.3k

Views

Why is rank $uv^{T}$ always equal to 1?

Published on 24 Oct 2016 - 9:33

score 768 · Answer 2 · 2016-10-29 00:10:27

768

Views

Matrix concepts

Published on 29 Oct 2016 - 0:10

score 3k · Answer 3 · 2016-10-31 17:23:32

3k

Views

Let $T : R^7 \to R^7$ be a linear transformation such that $T^2 = 0$

Published on 31 Oct 2016 - 17:23

score 191 · Answer 4 · 2016-11-02 03:38:46

191

Views

If $\lambda = i$ is an eigenvalue of $A \in \mathbb R^{n \times n}$, explain why the rank of $A^3 + A$ is less than $n$

Published on 02 Nov 2016 - 3:38

score 201 · Answer 5 · 2016-11-03 01:59:40

201

Views

property concerning singular matrix

Published on 03 Nov 2016 - 1:59

score 299 · Answer 6 · 2016-11-03 20:56:56

299

Views

Let A be $ m \times n$ and $B$ be $n \times p$, and suppose $AB = 0$. Explain why $\mathrm{rank}(A) + \mathrm{rank}(B) \leq n.$

Published on 03 Nov 2016 - 20:56

score 102 · Answer 7 · 2016-11-07 03:53:04

102

Views

Rank and matrix dimensions

Published on 07 Nov 2016 - 3:53

score 350 · Answer 8 · 2026-03-25 22:06:31

350

Views

Rank of kronecker product of partitioned matrix

Published on 25 Mar 2026 - 22:06

score 237 · Answer 9 · 2016-11-08 18:44:26

237

Views

A linear map $\varphi$ such that $\varphi (GL_n(\mathbb C) )\subseteq GL_n(\mathbb C)$ preserves the rank

Published on 08 Nov 2016 - 18:44

score 890 · Answer 10 · 2016-11-08 21:25:02

Prove that the rank of a nonzero $m \times n$ matrix $A$ is the largest number $r$ such that $A$ has an $r \times r$ minor with nonzero determinant.

score 973 · Answer 11 · 2016-11-12 22:00:06

973

Views

Show that if $ \operatorname{rank}(A) = \operatorname{rank}(A^{2}) $, then the algebraic and geometric multiplicities of $ \lambda = 0 $ are equal.

Published on 12 Nov 2016 - 22:00

score 25 · Answer 12 · 2026-03-27 22:31:14

25

Views

Minimal rank of a real algebra

Published on 27 Mar 2026 - 22:31

score 1.1k · Answer 13 · 2026-03-27 22:12:00

1.1k

Views

Singularity of a matrix times its transpose

Published on 27 Mar 2026 - 22:12

score 60 · Answer 14 · 2016-11-15 13:59:10

60

Views

Rank of a real matrix

Published on 15 Nov 2016 - 13:59

score 7.5k · Answer 15 · 2016-11-15 20:18:58

7.5k

Views

Rank of an incidence matrix of a graph G with n vertices is n-1 implies that G is connected

Published on 15 Nov 2016 - 20:18

List Question

Why is rank $uv^{T}$ always equal to 1?

Matrix concepts

Let $T : R^7 \to R^7$ be a linear transformation such that $T^2 = 0$

If $\lambda = i$ is an eigenvalue of $A \in \mathbb R^{n \times n}$, explain why the rank of $A^3 + A$ is less than $n$

property concerning singular matrix

Let A be $ m \times n$ and $B$ be $n \times p$, and suppose $AB = 0$. Explain why $\mathrm{rank}(A) + \mathrm{rank}(B) \leq n.$

Rank and matrix dimensions

Rank of kronecker product of partitioned matrix

A linear map $\varphi$ such that $\varphi (GL_n(\mathbb C) )\subseteq GL_n(\mathbb C)$ preserves the rank

Prove that the rank of a nonzero $m \times n$ matrix $A$ is the largest number $r$ such that $A$ has an $r \times r$ minor with nonzero determinant.

Show that if $ \operatorname{rank}(A) = \operatorname{rank}(A^{2}) $, then the algebraic and geometric multiplicities of $ \lambda = 0 $ are equal.

Minimal rank of a real algebra

Singularity of a matrix times its transpose

Rank of a real matrix

Rank of an incidence matrix of a graph G with n vertices is n-1 implies that G is connected

Trending Questions

Popular # Hahtags

Popular Questions