Matrix horizontal alignment

Question

I am trying to use the Gauss TeX package to display matrices. I have two problems with the following code (not so important):

    \usepackage{amsmath}
\usepackage{gauss}     
\begin{document}
\begin{equation}\begin{gmatrix}[b]
 1 & 0 & 0 & 0 & \frac{4}{5} & \text{\small{-}}\frac{3}{5} & \frac{2}{5} & \text{\small{-}}\frac{1}{5} \\
 0 & 1 & 0 & 0 & \text{\small{-}}\frac{3}{5} & \frac{6}{5} & \text{\small{-}}\frac{4}{5} & \frac{2}{5} \\
 0 & 0 & 1 & \frac{3}{4} & \frac{1}{4} & \text{\small{-}}\frac{1}{2} & \frac{3}{4} & 0 \\
 0 & 0 & 0 & 1 & \text{\small{-}}\frac{1}{5} & \frac{2}{5} & \text{\small{-}}\frac{3}{5} & \frac{4}{5}
\rowops
\add[\cdot ({-}\frac{3}{4})]{3}{2}
\end{gmatrix} \cong
\begin{gmatrix}[b]
 1 & 0 & 0 & 0 & \frac{4}{5} & \text{\small{-}}\frac{3}{5} & \frac{2}{5} & \text{\small{-}}\frac{1}{5} \\
 0 & 1 & 0 & 0 & \text{\small{-}}\frac{3}{5} & \frac{6}{5} & \text{\small{-}}\frac{4}{5} & \frac{2}{5} \\
 0 & 0 & 1 & 0 & \frac{2}{5} & \text{\small{-}}\frac{4}{5} & \frac{6}{5} & \text{\small{-}}\frac{3}{5} \\
 0 & 0 & 0 & 1 & \text{\small{-}}\frac{1}{5} & \frac{2}{5} & \text{\small{-}}\frac{3}{5} & \frac{4}{5}
\end{gmatrix}\end{equation}
\end{document}

It looks like this:

I bypassed the alignment a bit by using "\text{\small{-}}" in stead of "-", to make the fractions appear under each other, but they still don't line up quite nicely and the matrix need more vertical space but I cannot seem to figure out how to do this. Any help would be appreciated :-)

Answer 1

The gauss package seems to impede easy answers. Here's a solutions that isn't great but works: Replace all your \text{\small{-}} with \llap{-} (this will yield the alignment you desire), and add a strut to each row:

\documentclass{article}
\usepackage{amsmath}
\usepackage{gauss}
\newcommand\mystrut{\rule{0pt}{2.5ex}}
\begin{document}
\begin{equation}\begin{gmatrix}[b]
 1 & 0 & 0 & 0 & \frac{4}{5} & \llap{-}\frac{3}{5} & \frac{2}{5} & \llap{-}\frac{1}{5} \mystrut \\
 0 & 1 & 0 & 0 & \llap{-}\frac{3}{5} & \frac{6}{5} & \llap{-}\frac{4}{5} & \frac{2}{5} \mystrut \\
 0 & 0 & 1 & \frac{3}{4} & \frac{1}{4} & \llap{-}\frac{1}{2} & \frac{3}{4} & 0 \mystrut \\
 0 & 0 & 0 & 1 & \llap{-}\frac{1}{5} & \frac{2}{5} & \llap{-}\frac{3}{5} & \frac{4}{5} \mystrut
\rowops
\add[\cdot ({-}\frac{3}{4})]{3}{2}
\end{gmatrix} \cong
\begin{gmatrix}[b]
 1 & 0 & 0 & 0 & \frac{4}{5} & \llap{-}\frac{3}{5} & \frac{2}{5} & \llap{-}\frac{1}{5} \mystrut \\
 0 & 1 & 0 & 0 & \llap{-}\frac{3}{5} & \frac{6}{5} & \llap{-}\frac{4}{5} & \frac{2}{5} \mystrut \\
 0 & 0 & 1 & 0 & \frac{2}{5} & \llap{-}\frac{4}{5} & \frac{6}{5} & \llap{-}\frac{3}{5} \mystrut \\
 0 & 0 & 0 & 1 & \llap{-}\frac{1}{5} & \frac{2}{5} & \llap{-}\frac{3}{5} & \frac{4}{5} \mystrut 
\end{gmatrix}\end{equation}
\end{document}

(The builtin \strut is a bit too small, so I defined a larger \mystrut.)

Answer 2

One way to get more vertical space is to use \extrarowheight, in the array package. The syntax is \setlength{\extrarowheight}{x}, where x is a measure (e.g., 2pt, 3pt, etc). The effect only occurs if its value plus \baselineskipx\arraystretch is larger than the actual height of the cell. I usually add two or three points, and that makes the fractions come out suitably separated.