What does the notation $||u||$ mean?

Question

I know this is basic, but I am just a little unsure of this.

What does the notation $||u||$ mean? $u$ is a vector

It denotes the norm of $u$. Which norm that is depends. For $u \in \mathbb{R}^n$, it usually is $$\lVert u\rVert = \sqrt{\sum_{k=1}^n u_k^2}.$$ — Daniel Fischer, Dec 15 '13 at 18:24
Write $\|$ or $\parallel$ to generate $|$ or $\parallel$, which are the same thing anyway. — Mr Pie, Jun 20 '18 at 12:00

score 2 · Accepted Answer · answered Dec 15 '13 at 18:25

2

The generally accepted definition is $||\vec u||:=\sqrt{\vec u\cdot \vec u}$ where $\cdot$ is the dot product for vectors.

answered Dec 15 '13 at 18:25

Tim Ratigan

7,247

score 2 · Answer 2 · answered Dec 15 '13 at 18:25

2

It's the length of the vector. Assuming you have an inner product "$\cdot$" you can define it as $$ || u || = \sqrt{u\cdot u} $$

answered Dec 15 '13 at 18:25

Abramo

6,917

score 0 · Answer 3 · answered Jun 11 '14 at 12:55

0

That means Euclidean norm of a vector. Other names are Euclidean length, L2 distance, ℓ2 distance, L2 norm, or ℓ2 norm. This is a special case of Lp space. See Lp space

answered Jun 11 '14 at 12:55

aspirin

101
1

What does the notation $||u||$ mean?

3 Answers3