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

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
• It means magnitude of the vector. Useful list of symbols – Mufasa Dec 15 '13 at 18:24
• Thanks! I can see norm means the length also – Chrene Dec 15 '13 at 18:26
• Write $\|$ or $\parallel$ to generate $\|$ or $\parallel$, which are the same thing anyway. – Mr Pie Jun 20 '18 at 12:00

## 3 Answers

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

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

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