[Tex/LaTex] What’s the proper way to write a vector with a single character subscript

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I've always(-ish) thought that the proper way to typeset a vector which is labeled by a letter with a single character subscript, like v₁, was to set the arrow over just the letter, like \vec{v}_1 (I realize the braces are superfluous here but I like to include them for clarity). But recently I have seen it argued that this is wrong, and that the proper way is to place the arrow over the combination of the letter and subscript, with \vec{v_1}. I have done this in the past but I consider the results of the former method to be better looking.

Is there a standard recommendation to do this one way or another in the TeX world? Or is it a matter of personal preference?

EDIT: to put the question another way, suppose you're proofreading a LaTeX document, and suppose that all the notation is clearly defined so that there is no ambiguity about what v-with-subscript-1-and-arrow-over-it means:

If the author consistently writes \vec{v_1}, would you globally change it to \vec{v}_1?
If the author consistently writes \vec{v}_1, would you globally change it to \vec{v_1}?
Or neither of the above (i.e. it doesn't matter so respect the author's original preference)?

Best Answer

I don't believe there's a standard recommendation to answer your question, but it's probably not just a matter of personal preference either. A main criterion for good writing -- in any field, not just in mathematics! -- is the avoidance of all (unnecessary) ambiguity. One approach to keeping ambiguity low is to make sure that all symbols and notational conventions are explained at the outset. For instance, if you wrote something like

Let $\{\vec{v}_1,\vec{v}_2,\dots,\vec{v}_n\}$ denote a set of
$n$ elements of some vector space $V$.

in your paper, it should be clear to all readers that each \vec{v}_i, i=1,\dots,n, is a vector and that the subscript i merely serves to distinguish among the $n$ vectors. No further clarity would be gained, in my view, if the arrow symbol were shifted to the right to make it straddle both the v glyph and the subscript.

In contrast, suppose that the vector space V happens to be R^n and \vec{v} is some n-tuple. Now, there might be some ambiguity as to whether \vec{v}_i denotes the i-th element of v (i.e., a scalar) or the i-th n-tuple out of some set of n-tuples. If you need to refer to both types of variables in your paper, you might achieve a slight improvement in clarity by shifting the vector arrow to the right whenever you want to emphasize that you're dealing with an n-tuple rather than with a scalar.

To be sure, my recommendation in the second case would be to find a different notational solution altogether, in order to avoid any possible ambiguity. For instance, I might write v_i to denote the scalar quantity, i.e., I'd leave off the arrow entirely. I think that's much more direct and doesn't rely on your readers being alert enough to figure out on their own the meaning of a right-shifted arrow.

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