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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.

quanticle
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    Usually: tilde ("squiggle") below, or arrow above. – David Aug 19 '16 at 05:26
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    Put an arrow over it $\overset{\rightarrow}{V}$ – Gregory Grant Aug 19 '16 at 05:26
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    What about arrows over the vectors?? This is EXTREMELY common – Brevan Ellefsen Aug 19 '16 at 05:26
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    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. – pancini Aug 19 '16 at 05:29
  • Arrows make sense. I'm getting back into mathematics for the first time in a while, so I'm having to relearn a lot of the basic notational aspects. – quanticle Aug 19 '16 at 05:30
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    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. – Em. Aug 19 '16 at 05:31
  • Personally, I think there is no ambiguity if you use $x,y,w,v,u$ etc for vectors and $k,\lambda, \alpha, \beta$ etc for scalars (and $x_1,x_2,x_3$ etc for components, for example). It also works better for when you are not interested in becoming so much attached with the visual representation (or simply when you are not dealing with the vector space $\mathbb{R}^n$ ). – Aloizio Macedo Aug 19 '16 at 05:32
  • Some people use the hat, $\hat{v}$, but it has some other meanings, too. Personally, I vote for arrow. – MattW Aug 19 '16 at 05:39
  • for making writing easy, you may use capitals for matrices such as $A$, $B$, lower case letters for vectors $a$, $b$, $v$, and greek letters for scalars $\alpha$, $\beta$ etc.....this works if you work with few variables...however standard math notations are that given in above comments..such as arrows – user252783 Aug 19 '16 at 05:51
  • @MattWatkins Indeed. The hat is often used for unit vectors, including the orthonormal basis vectors $\hat\imath, \hat\jmath, \hat k, ..., \hat e_n$ $$\hat v = \dfrac{\vec v}{\lvert\vec v\rvert}$$ – Graham Kemp Aug 19 '16 at 06:44
  • The wavy line below the letter is standard typesetting mark-up for bold (as I learnt on this related thread). – Rob Arthan Aug 19 '16 at 19:42

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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.

Qiaochu Yuan
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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.

Rizky Reza Fujisaki
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    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.) – Graham Kemp Aug 19 '16 at 06:46
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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.]

David Quinn
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