What is the usual meaning of having the symbol $\hat{}$ (i.e., a hat) over a vector name? What do vectors denoted by $\hat{\mathbf{u}}$ usually represent?
For example, in this video, at min 3:00, the author denotes a unit vector by $\hat{\mathbf{u}}$, but I don't understand why not simply denoting it by $\mathbf{u}$. What is the difference between $\mathbf{u}$ and $\hat{\mathbf{u}}$?
Best Answer
In the video, at that very time, the speaker explains he is using that notation to point out $\hat{u}$ is a unit vector, i.e. a vector of norm $1$.
This sort of notations (once explained) helps remembering what are the specific properties of the quantities used in a proof. (Just looking at $\hat{u}$, you know it is unit.)
In linear algebra, the $\hat{}$ is widely used for unit vectors, so this is a general convention, at least in a good part of the world.