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In printed math texts, one can distinguish between scalar variable and vector variables because the vectors are in boldface. However, that doesn't seem to work as well when I take notes by hand. Is there an alternative standard for denoting vectors that is more suitable for handwritten notes? I find that I sometimes have trouble distinguishing between scalars and vectors in my handwritten notes, as it's not always clear from the context.

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    $\begingroup$ Usually: tilde ("squiggle") below, or arrow above. $\endgroup$ – David Aug 19 '16 at 5:26
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    $\begingroup$ Put an arrow over it $\overset{\rightarrow}{V}$ $\endgroup$ – Gregory Grant Aug 19 '16 at 5:26
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    $\begingroup$ What about arrows over the vectors?? This is EXTREMELY common $\endgroup$ – Brevan Ellefsen Aug 19 '16 at 5:26
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    $\begingroup$ the arrow is pretty common (often more of a check mark shape than an arrow with two points, for convenience). personally i wish we would just use arrows for all vectors instead of the bold face. $\endgroup$ – Elliot G Aug 19 '16 at 5:29
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    $\begingroup$ You could avoid this by clearly labeling which are scalars and which are vectors. If $\mathbb F$ is your field, then clearly write somewhere, $a,b,c\in\mathbb F$. If $V$ is the vector space, then $v,w\in V$. Otherwise, I try writing my scalars "straight" and my vectors cruly/slanted. $\endgroup$ – Em. Aug 19 '16 at 5:31
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I think many notations exist for a vector. Since I was undergraduate student, I use upper small arrow to indicate a vector, like this $\vec{v}$. In Japan, people use 'artificial white bold' letter, similar to this $\mathbb{V}$ (but small case, as if you want to write the notion for real number ($\mathbb{R}$)). I prefer using upper small arrow though.

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  • $\begingroup$ As a bonus, the $\vec v$ representation is nicely encoded in $\LaTeX$/mathjax as \vec v so it's also easy to remember and use. (For consistency between handwritten and screenwritten.) $\endgroup$ – Graham Kemp Aug 19 '16 at 6:46
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I just use different letters for them: typically $u, v, w$ for vectors and something like $x, y$, or $c$ for scalars. If there are a bunch I'll use subscripts, e.g. $v_i$ for a bunch of vectors and $c_i$ for a bunch of scalars.

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Underlining a letter to denote a vector quantity $\underline{v}$ is common practice and easier to write than arrows, and the text looks less cluttered.

Matrices are double-underlined $\underline{\underline{M}}$ when hand-written to distinguish them from vectors and from scalars which have no underline and are frequently Greek letters.

For example, you can write the eigenvector equation as: $$\underline{\underline{M}}\underline{v}=\lambda\underline{v}$$

[Someone who knows Mathjax better will be able to edit my double-underline to make it look neater.]

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