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  1. Is it customary to omit one pair of parentheses and write $T \begin{pmatrix} 1\\2\\1\\1 \end{pmatrix} $ instead of $T \begin{pmatrix} \begin{pmatrix} 1\\2\\1\\1 \end{pmatrix} \end{pmatrix}$ to indicate the image of $\begin{pmatrix} 1\\2\\1\\1 \end{pmatrix}$ under T ?

  2. When writing it out by hand, do you prefer the straight or curly underscore underneath "v" to indicate that v is a vector (as opposed to a scalar) ?

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As for your second question, I prefer not to use any special type of letter to indicate that something is a vector. Because then I have to think harder about the equations I'm looking at and the objects they involve. It may be a bit masochistic but I think it's helpful. –  Weltschmerz Jul 17 '12 at 13:45

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For (1), I would specify something like $v = \begin{pmatrix} 1\\2\\1\\1 \end{pmatrix}$, and then write $T(v)$. I think that omitting the parenthesis could be unambiguous, but writing $T \begin{pmatrix} \begin{pmatrix} 1\\2\\1\\1 \end{pmatrix} \end{pmatrix}$ frequently is going to get frustrating quickly.

For (2), in my experience, vector and matrix nomenclature depends very much on the field (as in subject matter, not algebraic structure).

Personally, in handwriting I prefer a harpoon over the symbol indicating that it is a vector. This is a personal preference question though, so probably best suited for community wiki.

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For (1), I've been masochistically sticking to the double pair of parentheses instead of omitting one pair or declaring the vector as v and then simply writing T(v), but yes it's getting really painful (and unsightly). For (2), I'm used to writing a harpoon over "AB" but a curly underscore beneath "v". Of late though, I've been finding that a straight underscore is much quicker to write than a curly, but it looks wrong to my unaccustomed eyes. –  Ryan Jul 17 '12 at 13:57
    
I quite like the notation $\vec{x}$ for vectors in handwriting as well. –  J. M. Jul 17 '12 at 14:01

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