What is the best symbol for vector/matrix transpose?

Question

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?

Answer 1

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}
$\mathbf{A}^\intercal$\\
$\mathbf{c}^\intercal \mathbf{x}$\\
$c^T x$\\
$\mathbf{M}^\top$
\end{document}

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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}

Answer 6

\documentclass{article}
\usepackage{amssymb,amsmath}
\usepackage{relsize}
\begin[document}
$A^T\ A^{\mathsmaller T}$
\end{document}

Answer 7

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^*.

Answer 8

I use the pre-exponent t in upright shape, either with mathtools package, based on the code: \prescript{\mathrm t}{}{A}, or using the \ltrans command from leftidx package. 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 \transp command, 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}

Answer 9

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

Answer 10

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.

Answer 11

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

Answer 12

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