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What is the best or most popular symbol for vector/matrix transpose? I have used simply ^T, for example $c^T x$. I think it is ugly, mainly because it is a little too big compared with vector variables usually denoted by lower-case characters. Can you suggest a better one?

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1  
Why does it look ugly? Too big? Too high? Too what? –  Werner Oct 5 '11 at 22:16
12  
That's exactly what I use! :) –  egreg Oct 5 '11 at 22:18
12  
I use M^\top. (For orthocomplements of vector spaces, I similarly use V^\bot.) Using T or t as a superscript is problematic in disciplines where they are modestly likely to occur as an actual variable, especially one which might occur in an exponent. I choose \top and \bot because they are more obviously abstract symbols, and not variables. –  Niel de Beaudrap Oct 5 '11 at 22:21
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(Incidentally, while I am opinionated on this subject, the very fact that it is strongly subject to opinion makes it a somewhat questionable topic for a StackExchange site...) –  Niel de Beaudrap Oct 5 '11 at 22:25
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Also, questions about mathematical notation are at best borderline on-topic. Maybe, @Chang, you can be more specific what you want to see. “I'm too lazy” is not a good way to ask questions here. –  Caramdir Oct 5 '11 at 22:27

12 Answers 12

up vote 44 down vote accepted

It's always difficult to answer questions for "the best" or "most popular". As is mentioned, these are typically opinions. But you did say that your objection was the fact that the "T" symbol was too big. Therefore, I would recommend the \intercal symbol to produce a "T" which isn't so big. Also, writing the vectors and matrices in bold seems, in my opinion, to make it look a little better. Try the following code:

\documentclass{article}
\usepackage{amsmath,amsfonts,amssymb}
\begin{document}
$\textbf{A}^\intercal$\\
$\textbf{c}^\intercal \textbf{x}$\\
$c^T x$\\
$\textbf{M}^\top$
\end{document}

Screenshot from example above

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9  
It is better to use \mathbf rather than \textbf –  Aditya Jul 16 '12 at 21:11
2  
An even better to defin a new command in sense of logical markup, i.e. use \vec and define \newcommand{\mtrx}[1]{\mathbf{#1}} –  Tobi Aug 13 '13 at 22:32
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And even even better to use \bm instead of \mathbf. 'Cause, you know, you never know what stupidly exotic symbol you might one day use as a matrix or vector to impress your supervisor, colleague, or yourself ;) (and in fact, \mathbf can't even handle Greek letters which aren't that exotic after all). –  Christian Jan 5 at 1:29

The Comprehensive LaTeX Symbol List says the following:

Some people use a superscripted \intercal for matrix transpose: A^\intercal. (See the May 2009 comp.text.tex thread, "raising math symbols", for suggestions about altering the height of the superscript.) \top, T, and \mathsf{T} are other popular choices.

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Thanks a lot! The book I am currently citing a formula from uses exactly what latex produces with \mathbf{w}^\top for a transposed vector. So I am going to go with this variant... (\intercal would be the second choice, but T and mathsf{T} look ugly in my opinion) –  Philip Daubmeier Jun 6 '12 at 15:12
    
I agree with those who suggest \intercal It looks like the traditional T for transpose, but at the same time it is not confused with the exponents. I am using it in my Tex-files. –  user37740 Oct 4 '13 at 16:45

enter image description here

\documentclass{article}
\usepackage{amssymb,amsmath}
\usepackage{relsize}
\begin[document}
$A^T\ A^{\mathsmaller T}$
\end{document}
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Personally I often use the conjugate transpose instead. For real matrices this concept coincides with the transpose, for matrices over the complex field the conjugate is usually what you want anyway. The conjugate transpose of a matrix A is denote A^*.

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Conjugate transpose is in physics often denoted by ^\dagger because of its association with adjoint operators.

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There are some good suggestions regarding which symbol to use, it is a good idea to define your own macros for indicating matrices, vectors, and transpose, so that you can write:

\MAT A \VEC b^\TRANSPOSE

This will make it easy to change the notation in the future, if you ever need to do so. In addition, the source is more readable than \mathbf A \mathbf b^\intercal etc.

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I prefer A^\mathsf{T} which looks clean and is the right size.

In my opinion, the serifs in A^T distracting, the T is set too low in A^\intercal, the T in A^\top is too thin and too big, and A^* implies the presence of complex numbers.

In any case, it's always good to use a macro in case you change your mind later.

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maybe you could use $\mathbf{C}^{^\mathrm{T}}$ to raise it a smaller transpose Tit produces this

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1  
Welcome to TeX.SX! –  Claudio Fiandrino Nov 7 '13 at 7:12

I use the pre-exponent t in upright shape, either with mathtools package, based on the code: \prescript{\mathrm t}{}{A}, or using the\ltranscommand fromleftidxpackage. Here is a code that tries to take into account different situations, which involve different math kerning, nested transpose, and so on. I define a\transpcommand, with an optional argument, the math kerning (defaults to-3mu`) between the t prescript and the ‘prescripted’ expression that follows.

\documentclass[12pt, a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools}

\newcommand*{\transp}[2][-3mu]{\ensuremath{\mskip1mu\prescript{\smash{\mathrm t\mkern#1}}{}{\mathstrut#2}}}%


\begin{document}

Matrix transposition has the following properties :
  \begin{align*}
\transp{(\mskip-1mu AB)} & = \transp{B}\transp{A} \\
\transp{(\transp{A})} & = A \\
\transp{(\mathrm N + \mathrm P)} & = \transp[0mu]{\mathrm N} +\transp[0mu]{\mathrm P}
\end{align*}

\end{document}

enter image description here

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2  
Could you give a complete MWE? –  Sean Allred Oct 5 '13 at 4:39
    
It is the first time I see the transpose as a presuperscript. Did you see it before. It is an interesting idea though to separate exponentiation and transposition (which commute for matrices). –  alfC Dec 31 '13 at 23:33
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@alfC: It's a traditional notation in French mathematical typography. Not the only one: there's also t or T as superscripts, but always in upright shape. –  Bernard Oct 7 at 11:51
    
@Sean Alfred: I had forgotten to add a full example. This is done now, and the code has been modified. –  Bernard Oct 7 at 12:59

A^{\tau} looks best for me. I tried others but T was still too big.

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In order to give some reference:

(DIN) EN ISO 80000-2:2013 writes it like the following.

% arara: lualatex

\documentclass{article}
\usepackage{mathtools}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\newcommand*{\matr}[1]{\mathbfit{#1}}
\newcommand*{\tran}{^{\mkern-1.5mu\mathsf{T}}}
\newcommand*{\conj}[1]{\overline{#1}}
\newcommand*{\hermconj}{^{\mathsf{H}}}

\begin{document}
\[\matr{A}\tran\]   

\[\matr{A}\hermconj\coloneqq(\conj{\matr{A}})\tran\]
\end{document}

The good part here is that the 'big' T visually fits to the H of the same size which might be used for the Hermitian conjugate matrix.

enter image description here

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The symbol \intercal is quite a nice symbol for transpose, but it is placed a little low. Therefore the example defines \transpose to use a \intercal, which is shifted to the baseline. The symbol size adapts to the current math style.

\documentclass{article}
\usepackage{amssymb}

\makeatletter
\newcommand*{\transpose}{%
  {\mathpalette\@transpose{}}%
}
\newcommand*{\@transpose}[2]{%
  % #1: math style
  % #2: unused
  \raisebox{\depth}{$\m@th#1\intercal$}%
}
\makeatother

\newcommand*{\test}[1]{%
  \[
    \mathbf{M}^{#1}
    \;
    \scriptstyle \mathbf{M}^{#1}
    \;
    \scriptscriptstyle \mathbf{M}^{#1}
  \]
}

\begin{document}
  \test{\transpose}
  \test{\intercal}
  \test{\mathsf{T}}
  \test{\top}
\end{document}

Result

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protected by Jubobs Dec 12 at 10:17

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