Vector notation
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For information on vectors as a mathematical object see vector (spatial). This page is about notation of vectors.
[edit] Declaration
A vector can be declared in three ways:
- Parentheses can enclose an ordered set of coordinates: (1,2,3).
- Angle braces can also enclose an ordered set:
- Unit vectors can be used to describe a vector more algebraically:
where 
are the unit vectors in each of the three dimensions.
A threespace vector was used for these examples, but the first two methods can be applied to any vector space. The unit vector notation however, is only common for 2 and 3 dimensional vectors as there are not standard unit vectors for higher dimensioned spaces.
Letters representing vector quantities are distinguished from scalar quantities by bolding them, for example ω represents the magnitude of a rotational velocity while ω represents a rotational velocity. When handwritten this is difficult to achieve, so several different notations are used. These include writing a tilde over or under the letter, and writing an arrow over the letter.
The origins of this come from the typographical convention of tilde-shaped or wavy underlining to represent bolding of text. Straight underlines are often lazily used to represent vectors but in typography these represent the italicising of charaters.
[edit] Products
There are three vector multiplications:
- The cross product is notated with the multiplication cross:
- The dot product is notated with the multiplication dot:
- Scalar multiplication is usually written implicitly to avoid confusion with the other two types of multiplication:
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