Correct notation for a versor

Question

I am writing an engineering thesis and I am in doubt about the correct notation for versors.

Is it a circunflex accent, an anticircunflex/caron accent or a breve?

I appreciate any comments you might have.

Answer 1

The point of mathematical notation is clear communication. Insofar as there is "correct" notation and "incorrect" notation, it comes down to whether or not the notation used achieves this goal of clear communication. There are typically two important ways of ensuring that your notation is clear:

1. Use standard notation when available. If one knows that there is standard notation for an object or idea, use that notation. Using non-standard notation is likely to cause confusion, as mathematicians have grown used to certain symbols and definitions. Changing things up is akin to using non-standard spelling—you can probably make yourself understood, but you are going to make it hard on your readers, so you probably shouldn't.

   For example, $\mathbb{N}$ is almost always used to denote the set of natural numbers, $|\cdot |$ typically denotes the absolute value of a real or complex number, and $f'$ generally denotes the derivative of a single-variable function $f$. Using these notations is unlikely to ever cause confusion.

2. Clearly define the notation being used. If one is not aware of standard notation, or if there is no standard notation, or if standard notation is going to cause confusion, then one has to introduce new notation. The key here is to very clearly define the notation before using it.

For versors, I am not aware of any standard notation. Of course, I didn't know what a versor was until I looked it up on Wikipedia (and I still don't know if this question is about unit quaternions or unit vectors more generally). Because I am not familiar with any standard notation, I would be comfortable introducing my own notation. Since a "hat" over a letter often denotes a unit vector, I like the following:

Definition: A versor is a vector (or quaternion) of unit length. Versors are distinguished from other vectors by a "hat". For example, given a vector $v$, the versor in the direction of $v$, denoted by $\hat{v}$, is the versor $$ \hat{v} = \frac{ v }{ | v | }, $$ where $|v|$ denotes the magnitude (norm, length, whatever) of $v$.

In $\LaTeX$, this is typeset as $\hat{v}$, which produces a circumflex.