putting two indices and exponents side to side

Question

I did not find the answer to my following question on the web. I apologize in advance if this question has already been answered somewhere. I would like to write a matrix with the two subscripts and exponents side by side, like in the following latex command.

${\left( T_{ij}\right)_{i=1}^n}_{j=1}^{p}$

However, in the command above, the indices and exponents are not at the same height. Does anyone know how to put them at the same height (while keeping them horizontally aligned)?

Answer 1

A workaround:

\documentclass{article}

\begin{document}
$ {            \left( T_{ij} \right)     _{i=1} ^{n} }
  { \vphantom{ \left( T_{ij} \right) } } _{j=1} ^{p} $
\end{document}

Remark:

• A \vphantom makes an invisible box with width zero, but the height and depth of the formula.

Answer 2

I would write it like a sum:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

$ \mathop{(T_{ij})}\limits_{i=1,\, j=1}^{n,\, p} $

\end{document}

Answer 3

A different solution, using a variant of smallmatrix; it can be adjusted to cope with higher parentheses:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newenvironment{lsmallmatrix}{\null\vcenter\bgroup
  \Let@\restore@math@cr\default@tag
  \baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
  \ialign\bgroup$\m@th\scriptstyle##$\hfil&&\thickspace
  $\m@th\scriptstyle##$\hfil\crcr
}{%
  \crcr\noalign{\vskip-.4ex}\egroup\egroup
}
\makeatother

\newcommand{\dbllimits}[3][.3ex]{%
  \begin{lsmallmatrix}
  #3\\[#1]
  #2
  \end{lsmallmatrix}
}

\begin{document}

\[
(T_{ij})\dbllimits{i=1 & j=1}{n & p} 
\left(\frac{i}{j}\right)\!\!\dbllimits[3ex]{i=1 & j=1}{n & p}
\]

\end{document}

However, I'd write this in one of the following two ways:

\[
(T_{ij})_{\substack{1\le i\le n\\[2pt] 1\le j\le p}}
\qquad
(T_{ij})_{1\le i\le n,\,1\le j\le p}
\]

Answer 4

We can make a macro \dblbounds with a simple syntax using the stackengine and xstring packages. Using in addition xparse, we can define a macro \multibounds that accepts any number of bounds as a list, with an even simpler syntax: only one argument, the different "bounds" are written with the same syntax as above, and separated by a semicolon:

\documentclass[a4paper, 11pt]{book}

\usepackage{mathtools}
\usepackage{xstring, xparse}
\usepackage{stackengine}

 \newcommand\dblbound[2]{\!\everymath{\scriptstyle}\setstackgap{L}{0.8\baselineskip}\Vectorstack[l]{\StrBehind{#1}{..} \StrBefore{#1}{..}}\:\Vectorstack[l]{\StrBehind{#2}{..} \StrBefore{#2}{..}}}

\newcommand\myVectorstack[1]{\def\stackalignment{l}\setstackEOL{..}\everymath{\scriptstyle}%
\raisebox{1pt}{\Vectorstack{\StrBehind{#1}{..}..\StrBefore{#1}{..}}}\:}
\DeclareDocumentCommand \multibounds
{ > { \SplitList { ; } } m}
{\!\ProcessList{#1}{\myVectorstack}}

\begin{document}

 \[%
 \left( T_{ij} \right)\dblbound{i = 1..n}{j = 1..p}%
\qquad
\begin{pmatrix}\displaystyle T_{i, j, k}\end{pmatrix}\multibounds{i = 1..n ; j = 1..p; k = 1.. q}{}
\]%

\end{document}