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I'm looking for a math symbol to represent the concatenation of two vectors: if x = (x1, x2) and y = (y1, y2) then x ? y = (x1, x2, y1, y2).

I'm not very much at home in vector calculus, so I don't know if there's a standard symbol for this. If not, then I remember from formal language theory that there's a round caret-like symbol for concatenating two strings, which would be fine for my purposes. I can't find it, though; the sources I've found online all recommend using juxtaposition for concatenation, but I'm afraid this would be mistaken for the dot product.

I'm using elsarticle.cls, so amsmath and amssymb are both available.

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I math it is often written as (x,y), with an implicit identification of ℝ²×ℝ² and ℝ^4. –  Caramdir Jan 6 '11 at 15:42
    
@Caramdir: if you post this as an answer, I'll accept it. –  larsmans Jan 6 '11 at 16:09
    
Ben seems to already have done that. Harold's suggestion is also common, using (more or less) the same identification. –  Caramdir Jan 6 '11 at 19:04
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3 Answers 3

up vote 2 down vote accepted

Since a vector in R^2 is written (1, 2), it would make sense to concatenate two vectors a and b as (a,b).

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This is also how it's done in some programming languages, e.g. Matlab. –  Ben Jan 8 '11 at 0:36
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Personally, I would use \oplus for this. I would think of it as a direct sum of two vectors (as a member of the direct sum of two vector spaces).

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You can use two pluses joined together, which is rather intuitive

\documentclass[a4paper]{article}
\newcommand{\concat}{\ensuremath{+\!\!\!\!+\,}}
\begin{document}
$a \concat b$
\end{document}

Another symbol is ||

 \[ p\|q=p b^{l(q)}+q \]

The \| command gives a double vertical bar.

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