Avoiding overlapping superscripts and subscripts in matrices

Question

I was working on some calculus today and tried to typeset a matrix of partial derivatives and ran into some trouble. Here is my code:

\documentclass{minimal}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{pmatrix}
    \frac{\partial f^1}{\partial x_1}   & \frac{\partial f^1}{\partial x_2}\\
    \frac{\partial f^2}{\partial x_1}   & \frac{\partial f^2}{\partial x_2}
\end{pmatrix}
\end{equation}
\end{document}

As can be seen, the output results in the subscripts from the denominators of the top row on the matrix with the superscripts from the numerators of the bottom row on the matrix. Is there an easy way to avoid this?

Answer 1

The cellspace package defines 2 lengths, \cellspacetoplimit and \cellspacebottomlimit that are the minimal vertical white space between the top of a cell and the bottom of the above cell, and between the bottom of a cell and the top of the below cell. Here is a example:

    \documentclass{minimal}
    \usepackage{mathtools}

    \usepackage[math]{cellspace}
    \cellspacetoplimit 3pt
    \cellspacebottomlimit 3pt
    \setlength{\arraycolsep}{4pt}
    \begin{document}
    \[
    \begin{pmatrix}
        \dfrac{\partial f^1}{\partial x_1}   & \dfrac{\partial f^1}{\partial x_2}\\
        \dfrac{\partial f^2}{\partial x_1}   & \dfrac{\partial f^2}{\partial x_2}
    \end{pmatrix}
    \]

    \cellspacetoplimit 0pt
    \cellspacebottomlimit 0pt
    \[
    \begin{pmatrix}
        \dfrac{\partial f^1}{\partial x_1}   & \dfrac{\partial f^1}{\partial x_2}\\
        \dfrac{\partial f^2}{\partial x_1}   & \dfrac{\partial f^2}{\partial x_2}
    \end{pmatrix}
    \]
    \end{document} 

It works with the amsmath environments (matrix, &c.), but not, unfortunately, with their starred versions defined by mathtools.

Answer 2

One way is to use the optional argument of \\ like \\[<length>]:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{pmatrix}
    \frac{\partial f^1}{\partial x_1}   & \frac{\partial f^1}{\partial x_2}\\[1ex]
    \frac{\partial f^2}{\partial x_1}   & \frac{\partial f^2}{\partial x_2}
\end{pmatrix}
\end{equation}
\end{document}

Another way is to add one invisible line with 0 width, -2ex depth (say) and 4ex total height in the first row.:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{pmatrix}
    \rule[-2ex]{0pt}{4ex}\frac{\partial f^1}{\partial x_1}   & \frac{\partial f^1}{\partial x_2}\\
    \frac{\partial f^2}{\partial x_1}   & \frac{\partial f^2}{\partial x_2}
\end{pmatrix}
\end{equation}
\end{document}

Answer 3

With a TABstack, you have complete control over the horizontal and vertical spacing. Here are two examples.

\documentclass{minimal}
\usepackage{tabstackengine}
\begin{document}
\begin{equation}
\setstackgap{L}{1.6\baselineskip}
\setstacktabbedgap{1ex}
\parenMatrixstack{
    \frac{\partial f^1}{\partial x_1}   & \frac{\partial f^1}{\partial x_2}\\
    \frac{\partial f^2}{\partial x_1}   & \frac{\partial f^2}{\partial x_2}
}
\end{equation}
\begin{equation}
\setstackgap{L}{1.8\baselineskip}
\setstacktabbedgap{1.4ex}
\parenMatrixstack{
    \frac{\partial f^1}{\partial x_1}   & \frac{\partial f^1}{\partial x_2}\\
    \frac{\partial f^2}{\partial x_1}   & \frac{\partial f^2}{\partial x_2}
}
\end{equation}
\end{document}