I want to know if a vector should look like $\mathbf{v}$ (upright) or $\boldsymbol{v}$ (italic). The 1999 note "On the use of italic and roman fonts for symbols in scientific text" (PDF link via iupac.org) from the IUPAC Interdivisional Committee on Nomenclature and Symbols says:
Vectors, tensors and matrices are usually denoted using
a bold-face (heavy) font, but they should still be italic since they are still quantities.
However, Wikipedia's "Euclidean vector" entry uses an example of a vector that looks like this:
As you can see, the $\mathbf{a}$ is upright. However, the same article also said:
Vectors are usually denoted in lowercase boldface, as a or lowercase italic boldface, as a.
But I’ve noticed that Wikipedia mainly uses upright vectors, and most of the math I’ve seen uses upright vectors as well.
To me, it seems like conventions agree that one should write vectors in italics, but in practice, it seems like vectors are written upright most of the time.
So should vectors be written in italics or upright?
Note: this question looks a bit like this one, however I don’t think that they are duplicates. The other question is asking about Greek letters while my question is asking about symbols for vectors in general.
Best Answer
This is a great notation question. However, my answer aims to draw your focus to the fact that it depends on the author and how you are viewing the literature.
In most articles and books I have read via a computer, at least recently, vectors are denoted in bold-face (heavy) font such as v. However, as stated in the comments this poses challenging when writing down a vector with a pencil. To accommodate this, the physicist may write a vector as $\vec v$ (which employs the italic font as well). Writing a vector upright is a good way to solve all of this - being quick and easy. As long as you specify that indeed the object $v$ is a vector by writing something such as "let $v \in \mathbb{R}$" (for example).