Let us say that we have a vector $\vec{v} = \langle 1 + i, i \rangle$. As far as I am aware, using the arrow above the vector as done above is how vectors are generally denoted in writing and also in LaTeX (as it corresponds to the \vec command). Textbooks, however, often use a bolded letter, e.g. $\mathbf{v}$, to denote vectors.

Let's say that I want to denote the complex conjugate of the vector above. To denote the complex conjugate of an expression, I've seen bars normally being used, e.g. $\bar{z}$ or $\overline{a + bi}$.

How would I write the complex conjugate of vector $\vec{v}$? In handwriting, I feel like I should simply put a bar over the vector, like $\overline{\vec{v}}$, but this does not looks very nice and seems to hinder communication. I assume I could also write $\overline{\langle 1 + i, i \rangle}$, but I'm looking for a way to denote the conjugate of the vector letter itself. Textbooks I understand probably can get away with writing $\bar{\mathbf{v}}$.

So what is the "proper" way to denote the complex conjugate of some vector in handwriting?

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    $\begingroup$ Most math authors don't put arrows over vectors. So then if $x$ is a vector in $\mathbb C^n$, you could use the notation $\bar x$ for the componentwise complex conjugate of $x$. $\endgroup$ – littleO Nov 21 '18 at 3:36
  • $\begingroup$ @littleO I think that's about as close to an answer as OP can expect. Perhaps promote your comment to a full answer? $\endgroup$ – Travis Nov 21 '18 at 6:18
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    $\begingroup$ If you always write arrows over your vectors and conjugating a vector is not a surprise (because it’s mentioned in the surrounding text or a natural thing to do in the specific situation), I don’t think the arrow plus overbar will be confusing. I would make sure that the overbar is longer than the arrow (to “cover” it) but then you’re fine. (It still doesn’t look nice, though.) $\endgroup$ – Eike Schulte Nov 21 '18 at 12:55

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