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

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

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    $\begingroup$ It denotes the norm of $u$. Which norm that is depends. For $u \in \mathbb{R}^n$, it usually is $$\lVert u\rVert = \sqrt{\sum_{k=1}^n u_k^2}.$$ $\endgroup$ – Daniel Fischer Dec 15 '13 at 18:24
  • $\begingroup$ It means magnitude of the vector. Useful list of symbols $\endgroup$ – Mufasa Dec 15 '13 at 18:24
  • $\begingroup$ Thanks! I can see norm means the length also $\endgroup$ – Chrene Dec 15 '13 at 18:26
  • $\begingroup$ Write $\|$ or $\parallel$ to generate $\|$ or $\parallel$, which are the same thing anyway. $\endgroup$ – Mr Pie Jun 20 '18 at 12:00
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The generally accepted definition is $||\vec u||:=\sqrt{\vec u\cdot \vec u}$ where $\cdot$ is the dot product for vectors.

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

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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

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