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I am wondering if there is any standard notation for the element-wise division of vectors.

I am going to use $\oslash$ for this purpose, similar to $\odot$ that is used in some texts for element-wise multiplication. For example, assuming $\vec{u}$ and $\vec{v}$ are vectors of length $k$, then $\vec{x} = \vec{u} \oslash \vec{v}$ if $\vec{x}(i) = \vec{u}(i) / \vec{v}(i)$. Would that be strange to use this in a scientific paper?

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    Typically, I would shy away from introducing new notation. You can accomplish the same result by left-multiplying the vector by a diagonal matrix whose entries are the divisors.2012-07-18
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    Octave/Matlab use $u./v$. Not pretty, but might be more recognizable, depending on your audience.2012-07-18
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    I agree with @Ed. If you feel like dividing or multiplying vectors componentwise, they are not vectors to you any more. They are diagonal matrices. Notice that you don't lose anything by switching to matrices: addition, scalar multiplication and scalar product still work fine. You can write diag(a,b,c) when the entries need to be listed.2012-07-18

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