String/vector concatenation symbol

Question

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.

I math it is often written as (x,y), with an implicit identification of ℝ²×ℝ² and ℝ^4. — Caramdir, Jan 06 '11 at 15:42
Ben seems to already have done that. Harold's suggestion is also common, using (more or less) the same identification. — Caramdir, Jan 06 '11 at 19:04

score 11 · Answer 1 · answered Jan 06 '11 at 16:07

11

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).

answered Jan 06 '11 at 16:07

Harald Hanche-Olsen

15,968

Plus you can use \bigoplus to easily represent the concatenation of multiple vectors! – Vivek Aug 04 '21 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). – Mateen Ulhaq Dec 05 '23 at 02:41

score 6 · Answer 2 · edited Nov 20 '11 at 00:12

6

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.

edited Nov 20 '11 at 00:12

Werner

603,163

answered Jan 06 '11 at 15:13

yannisl

117,160

score 5 · Accepted Answer · answered Jan 06 '11 at 17:44

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).

answered Jan 06 '11 at 17:44

Ben

2,609

This is also how it's done in some programming languages, e.g. Matlab. – Ben Jan 08 '11 at 00:36

score 1 · Answer 4 · answered Apr 22 '20 at 05:05

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.

String/vector concatenation symbol

4 Answers4

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