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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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  • 3
    I math it is often written as (x,y), with an implicit identification of ℝ²×ℝ² and ℝ^4.
    – Caramdir
    Commented Jan 6, 2011 at 15:42
  • Ben seems to already have done that. Harold's suggestion is also common, using (more or less) the same identification.
    – Caramdir
    Commented Jan 6, 2011 at 19:04
  • Here is the same question on Math SE.
    – Albert
    Commented Oct 21, 2014 at 13:40
  • \frown! That's it.
    – Fred Foo
    Commented Oct 21, 2014 at 16:12

4 Answers 4

5

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
    Commented Jan 8, 2011 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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  • Plus you can use \bigoplus to easily represent the concatenation of multiple vectors!
    – Vivek
    Commented Aug 4, 2021 at 13:20
  • This notation doesn't really work that well for tensors, since they must be concatenated along only one axis (which is not specified by this notation). Commented Dec 5, 2023 at 2:41
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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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Computer science often uses the ⧺ (U+29FA) symbol. (String concatenation is ++ in the Haskell programming language, to represent this.)

This is \doubleplus in unicode-math and the legacy packages stix and stix2. Or, in the modern toolchain, you can use the Unicode symbol in your source.

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