The Transpose Correct (or Mostly Agreed Upon) Notation Concern

Question

I am writing this question as a follow up of the discussion in this question here Where the most voted answer suggested the following as possible transpose notations

My main concerns are the following :

1. The $A^{T}$ is problematic when I use it because I have a matrix $T$ and I could end up with $T^{T}$ which is misleading and can not avoid that.

2. The $A^{\top}$ is problematic as it resembles the tangential part symbol.

3. The $\mathsf{T}$ appears to display an obvious capital T which resembles the issue in (1)

4. The $A^{intercal}$ looks almost perfect however, I have some concerns which are my two questions :

A) How can we reduce the spacing between the matrix A and the transpose symbol $\intercal$ as it looks too spaced in this case?

B) How can we adjust the height of the transpose symbol $\intercal$ ? since it appears here too low and this was recommended in the following reference page 30 but presented without any demonstration.

I would like to add that I only use bold font capital letters when I want to draw a matrix and define it by a capital letter and not when I am writing a proof. Therefore, my question is strictly concerned towards the writing of the transpose notation during writing expressions,proofs,...

Answer 1

However you want to denote a transposed matrix I suggest you define a macro, which you can change afterwards. I'm not sure there is an easy way to get the correct horizontal placement right under any circumstance. I'd go with an optional parameter, something like this:

\documentclass{article}

\usepackage{amssymb}

\makeatletter
\newcommand*{\transpose}{\bgroup\@transpose}
\newcommand*{\@transpose}[1][0]{\mathpalette\@@transpose{#1}\egroup}
\newcommand*{\@@transpose}[2]{\setbox0=\hbox{\m@th$#1\mkern-#2mu\intercal$}\raise\dp0\box0}
\makeatother

\begin{document}

% With \intercal symbol
$A^{\intercal}$ $\mathbf{A}^\intercal$

% With \transpose
$A^\transpose$
$\mathbf{A}^{\transpose}$
$\mathbf{A}^{\transpose[4]}$
$M^\transpose$
$\mathbf{M}^\transpose$

\end{document}

The triple macro definition is needed in order for A^\transpose to work (though that is considered bad style).

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Alternatively, a simplified version which discriminates only between starred/unstarred: less fine control but also less typing.

\documentclass{article}

\usepackage{amssymb}

\makeatletter
\newcommand*{\transpose}{\bgroup\@ifstar{\mathpalette\@transpose{\mkern-3.5mu}\egroup}{\mathpalette\@transpose\relax\egroup}}
\newcommand*{\@transpose}[2]{\setbox0=\hbox{\m@th$#1#2\intercal$}\raise\dp0\box0}
\makeatother

\begin{document}

$A^\transpose$
$\mathbf{A}^\transpose$
$\mathbf{A}^{\transpose*}$
% $\mathbf{A}^\transpose*$ % works too but it's very very bad style

$M^\transpose$
$\mathbf{M}^\transpose$

$\mathbf{L}^\transpose$
$\mathbf{L}^{\transpose*}$

\end{document}

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Incidentally, I fully agree with egreg's comment that changing notation within a paper is a very evil thing (well, he hasn't exactly said that, but I'm sure he thinks it :-)).