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.
Is there a standard way of distinguishing between scalars and vectors in handwritten notes?
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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.]
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.