Hopefully a basic question. Through undergraduate study we tended to use either juxtaposition or a dot to symbolise multiplication. The whole class put the dot in the middle vertically when doing this until we got to vectors and were introduced to the dot product.

the lecturer said "he thinks" that the correct way of writing the two types (dot product vs your common multiplication with dot notation) is that you put the dot in the middle vertically for dot product, and at the bottom for common multiplication.

Just wondered what the correct notation is...

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    $\begingroup$ There's probably as many notations as people. As long as something has been defined though, the notation should be respected. $\endgroup$ – Klangen Aug 29 at 9:37
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    $\begingroup$ The issue is that when you write by hand is not so easy to write the dot vertically in the middle versus vertically bottom... $\endgroup$ – Mauro ALLEGRANZA Aug 29 at 9:40
  • $\begingroup$ Maybe some such considerations were behind the standardization of mere juxtaposition for multiplication, something which, I must confess, has always seemed rather incomplete to me, since the operation of multiplication isn't itself denoted as in all the other arithmetic operations, until now! $\endgroup$ – Wd Fusroy Aug 29 at 9:48

I believe it really depends on the context. If you are working with a multiplicative group $(G,\cdot)$, then you should write $a\cdot b$ everytime you multiply two elements $a,b \in G$. If it is clear these two elements are from $G$, or it is not necessary to specify the operation, you can just write $ab$. If $G$ has the structure of vector space, you may want to use the notation $\langle v,w \rangle$ instead of $v\cdot w$ for the dot product of two vectors $v,w$.


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