What is the best way to take a transpose of a matrix with superscripts and subscripts, when the subscript is long?
Neither
$A_{ijk}^{a\top}$
$A_{ijk}^{a^{\top}}$
${A_{ijk}^{a}}^{\top}$
${A^{a}}^{\top}_{ijk}$
seems to have the same spacing and size as $B_{ijk}^{\top}$
I'm assuming you wish to denote the transpose of a matrix with \top. Then, if the matrix is written as A_{ijk}^{a}, you may want to write its transpose as {A_{ijk}^{a}}^{\!\!\top}. The \!\! directive (two negative-thinspaces) serves to "snug up" the superscript-\top to the associated matrix.
If you have many matrix transpose expressions, it's useful to create a macro (called \tp in the example below) to speed up the typing process. The default amount of "snugging up" is set to \mkern-6mu, which is equivalent to \!\!, i.e., to two negative thinspaces. The \tp macro is set up to take an optional argument, to let you vary the amount of "snugging up" on a case-by-case basis.
\documentclass{article}
\newcommand\Amat{A_{ijk}^{a}}
\newcommand\tp[2][-6]{{#2}^{\mkern#1mu\top}} % 'transpose' macro
\begin{document}
\[
\Amat
\quad
{\Amat}^{\!\!\top} % '\!\!' is equivalent to '\mkern-6mu'
\quad
\tp{\Amat} % use '\tp' macro
\quad
\tp{\Amat} \! \Amat % inner product of \Amat with itself
\quad
\tp[-9]{\Amat} % tighter spacing: -9mu instead of -6mu
\]
\end{document}
This question seems as much mathematical as it is typographic, by which I mean that the typographic rendering should follow (somewhat) logically from the mathematical meaning. So you need to think about what exactly you are transposing, and then ask how best to place the ^\top to indicate that meaning. In the case of matrices—so just two indices—I prefer
$(A^\top)_{ij} = A_{ji}$
rather than
$(A_{ij})^\top = A_{ji}$
The first says states the mathematical truth that the ij-th entry of A-transpose is the ji-th entry of A. The second is problematic because A_{ij} is just a number, and the transpose of a number is itself.
Because you have more than two indices—{ijk} below, and {a} above—it's not clear on which part of all that you wish ^\top to act. You may need to insert some parentheses to clarify. For example,
$({A_{ij}}^\top)_k^{a} = ({A_{ij}}^\top)_a^{k}$
ijk. Can you adapt your answer to incorporate this aspect?
– Mico
Sep 28 '18 at 16:30
A which is identified by i,j,k.
– user15988
Sep 28 '18 at 16:51
\tp macro, you might try \tp[-4]{(\Amat)}. I made use of his optional argument to change the kerning from his default -6 to the slightly looser -4, which I happen to think looks better with the closing parenthesis.
– iron photon
Sep 28 '18 at 18:15
a. It is more evident when you use\astinstead of\top. – user15988 Sep 28 '18 at 15:51A_{ijk}^{a^{\ast}}, but with the same size asA_{ijk}^{\ast}. – user15988 Sep 28 '18 at 15:58A_{ijk}^{a^{\scriptstyle\ast}}? – Ian Thompson Sep 28 '18 at 16:02