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Is there any established notation to abbreviate $\vec{x}/||\vec{x}|| = \frac{\vec{x}}{||\vec{x}||}$? Sure, this expression looks quite short already, but with a long argument such as $\vec{x} = a\cdot (\vec{b} \times \vec{c}) - (\vec{c} \cdot \vec{d}) \cdot \vec{e} + \frac{\vec{f} \cdot \vec{g}}{||\vec{f}|| \cdot ||\vec{g}||} \cdot \vec{h} + \dots$ it becomes hard to read very fast. I am thinking of something as $(\vec{x})_u$ or so.

Such a notation would not only simplify $\vec{x}/||\vec{x}||$, but also the $\frac{\vec{f} \cdot \vec{g}}{||\vec{f}||\cdot||\vec{g}||}$ in the argument $\vec{x}$. Also, repeating the same long expression is not too polite, since a reader might feel the need to look for small, but significant differences between the nominator and the denominator.

bers
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    There is no standard way to do so, but you could define this yourself i.e. $$x_\nu := \begin{cases}\frac{x}{\Vert x \Vert} & x\neq 0\ 0 & x=0\end{cases}$$ – AlexR Sep 13 '13 at 12:08
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    I don't believe there's a standard notation. If you want to make your writing more succinct, just say at the beginning of an arguement: Let $n(\vec{x})=\frac{\vec{x}}{||\vec{x}||}$ for all $\vec{x}\neq 0$. – Dan Rust Sep 13 '13 at 12:08
  • To my knowledge, there is not any standard notation, at least in linear algebra literature, for a normalised vector. Of course, that doesn't rule out the existence of such a notation in the literature of other research disciplines. – user1551 Sep 13 '13 at 12:11

1 Answers1

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If you switch to using boldface font for vectors, e.g., $\mathbf x$ rather than $\vec x$, then it is reasonable (and common in physics/engineering circles) to use the notation $$\hat{\mathbf x}=\frac{\mathbf x}{\|\mathbf x\|}$$ It's right at the beginning of the Wikipedia article Unit vector.

user103402
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    Great, but if you do use vector notation then $$\hat{\vec{x}}$$ is rather ugly.

    I have seen $$\langle \vec{x} \rangle$$ sometimes though.

     – John Alexiou May 02 '16 at 16:25