Is "hat notation" for unit vectors commonly used in mathematics?

Question

As an undergraduate, I clearly remember learning and using "hat notation" to describe unit vectors. That is, if $\vec{v}$ is any vector (in 2 or 3 dimensions) then $\hat{v}$ denotes the unit vector in the direction $\vec{v}$, i.e. $$\hat{v} = \frac{\vec{v}}{|\vec{v}|}$$

The "hat" was also used for the standard unit vectors in the direction of the $x$-, $y$-, and $z$-coordinate axes: $$\hat{i}=\langle 1,0,0 \rangle,\quad \hat{j}=\langle 0,1,0\rangle, \quad \hat{k}=\langle 0,0,1\rangle$$

Now that I am teaching multivariable calculus for the first time, I see no use of this notation in our textbook (Stewart, 8th Ed.), and I am wondering if this notational convention is something I picked up from my undergraduate Physics coursework. (Just to avoid misunderstanding: Stewart uses boldface $\bf{i}$,$\bf{j}$,$\bf{k}$ for the unit vectors but does not use the hat accent.) So my questions:

Is "hat notation" for unit vectors (including the standard unit vectors, but not limited to them) widely used in teaching multivariable calculus, or is this something only physicists use? Are there math textbooks that use it?

Edited to add: I thought I would mention the main reason I'm interested in this notation: it makes certain formulas involving projection much simpler. For example, if $\vec{u}$ and $\vec{v}$ are any two vectors then $$\operatorname{proj}_{\vec{u}}\vec{v} = \vec{v} \cdot \hat{u}$$ $$\operatorname{comp}_{\vec{u}}\vec{v} = \left(\vec{v} \cdot \hat{u}\right) \hat{u} $$

(compare $\frac{\vec{v} \cdot \vec{u}}{|\vec{u}|}$ and $\frac{\vec{v} \cdot \vec{u}}{|\vec{u}|^2}\vec{u}$, respectively). Likewise the angle between any two vectors $\vec{u}$ and $\vec{v}$ is given by $\cos(\theta) = \hat{u} \cdot \hat{v}$.

Answer 1

I wouldn't say it's common (none of the calculus books on my shelf use it). It's in some math books (e.g., this one, and this one and this one) but it's mostly in physics books.

Answer 2

Echoing other comments and @ncr's answer: this notational convention is not unknown, but is not common in mathematical contexts.

Perhaps more to the point, although relatively experienced math people might guess what is intended, they'd need to ask to proceed with confidence, so whatever time was thought to be saved by the convenient notation might be lost by having to answer questions about it.

Also, the very-very-common convention to use "hat" for Fourier transform should give the Fourier-transform use vast precedence over a relatively trivial use of giving the unit vector corresponding to a vector, in my opinion. (The fact that people typically talk about vectors for a while before learning about Fourier transforms doesn't alter my opinion. It's not good to have temporary notation that becomes wildly misleading soon after.)