vector notation – why is overhat notation used both for a unit vector, $\hat{\mathbf x} = {\mathbf x \over || \mathbf x ||}$, and for the closest vector in a subspace $\hat{\mathbf x}$ to a vector $\mathbf x$, related to the best approximation theorem in linear algebra.
I know that notation is developed by many people over time and confusing notation arises, but I am wondering if there is any rationale or reason or preference for one of these uses of the 'over hat' compared to the other.
looked at related question
What's the meaning of having ^ over a vector name?
but it does not answer this point as it does not refer to the use of the closest approximation vector.
Best Answer
I think it's a coincidence. There are just a few ways to mark a mathematical object as related to or sort of like one you have. You can write $x'$ or $\hat x$ or $\bar x$ or $x^*$ and a few others. Mathematicians in unrelated parts of the subject have chosen meanings for these annotations they find useful. Since there are more areas than markings there's bound to be some overlap.