I understand the notation of upper and lower indices for components of vectors and covectors, but when I write a vector not in component form I use an over-arrow notation e.g. $\vec r$. Is there a standard notation for covectors? An under-arrow? A left arrow?
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1I don't think there is a companion to $\vec{(\cdot)}$ (or boldface, or underline, or wavey underline, ...) for covectors. You can borrow the bra-ket convention from theoretical physics if you want. – user10354138 Apr 12 '21 at 02:42
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Covectors are also vectors so they can also be typeset with an arrow overhead. They are usually distinguished from vectors by using the greek alphabet.
So $\vec v$ for a vector
And $\vec \alpha$ for a covector.
Having said this, I've never seen covectors being notated in this way.
Mozibur Ullah
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I'm not sure this is correct. The covector lives in the dual space. I may make an identification of the covector with a vector in the vector space e.g. $f^\mu = g^{\mu\nu}f_\nu$, but that's not quite the same thing. – Kieran Mullen Apr 12 '21 at 04:26
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@Kieran Mullen: Given a vector space $V$, the dual space $V^$ is also* a vector space. It's obviously not the same space as the original space, that is $V$ is not the same as $V^$, nevertheless, $V^$ is a vector space. – Mozibur Ullah Apr 12 '21 at 05:29