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Is there a difference in the dot (position, size, etc) used in the vector dot product vs the one use for multiplication?

For typesetting here we use \cdot for both, i.e. $$2\cdot 3$$ or $$\mathbf u\cdot \mathbf v$$ Would that that be correct or is there an more proper alternative?

For instance, in addition to \cdot ($\cdot$) there is also \bullet ($\bullet$).

J. W. Tanner
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Hypergeometricx
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    In my experience -- no. I personally use \cdot for both, and I haven't noticed any difference in any textbooks/papers I've read. I suspect most people use \cdot for both, off the top of my head – HallaSurvivor Dec 03 '20 at 05:19
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    A search for dot product on the TeX StackExchange shows results that could be helpful. FYI, I also use \cdot dot- and arithmetical-products (also sometimes \times ($\times$) in arithmetical contexts), though I'd prefer a "beefier" dot product symbol without the heft of \bullet. (Answers to this TeX.SE question suggest how to make one.) If you're submitting to publishers, then individual journals may have specific guidelines about which symbol is appropriate. – Blue Dec 03 '20 at 05:55

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Note that typical multiplication is really a special case of dot product in one dimension. In other words, if $x = (x_k)_{k=1}^n$ and $y = (y_k)_{k=1}^n$ with $x,y \in \mathbb{R}^n$, then $x \cdot y = \sum_{k=1}^n x_k y_k$, so if we are doing this in 1D, we have $x\cdot y = x_1y_1$.

This will explain why the notation is the same.

gt6989b
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  • Does this logic also apply to the cross product? We see the "$\times$" symbol used to represent multiplication along with "$\cdot$", which you have already explained, so does that mean that multiplication using the cross symbol is describing a special case of the cross product in one dimension? – Kalcifer Feb 03 '21 at 01:43
  • @Kalcifer yes, but it is more funky: $(a,0,0) \times (0,b,0) = (0,0,ab)$ – gt6989b Feb 03 '21 at 14:51