As percusse points out, you can resize it using the package graphicx:
{\raisebox{-1.5ex}{\scalebox{3}{$\mathcal{A}$}}}
However, I would say that it looks better "small" than "resized". That would be very inconsistent and weird. I recommend you to stuck with small $A$. However, there're few possible improvements of your code:
\documentclass{report}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\begin{document}
\[ \begin{pmatrix}
| & & | \\
f_1 & \cdots & f_n \\
| & & | \end{pmatrix} \mathcal{A} =
\begin{pmatrix}
| & & | \\
q_1 & \cdots & q_n \\
| & & | \end{pmatrix}\]
\end{document}
- Do not use
ngerman package, use babel with the appropriate option.
- The package
amsmath offers the environment pmatrix for matrices in parentheses, as well as bmatrix for [...], Bmatrix for {...}, vmatrix for |...| and Vmatrix for ||...||.
- I'm not sure what the verical bars denote (probably a vector written in a column?) but I'm sure I would not understand it as a reader. However, I don't know how to improve it, since the context is missing. If the entries are really column vectors and you defined them properly before, I think that the reader would understand it even without the bars.
graphicxpackage, you can use{\raisebox{-1.5ex}{\scalebox{3}{$\mathcal{A}$}}}but the result would not look that nice I guess. – percusse Dec 4 '12 at 18:16smallmatrixvariants. – percusse Dec 4 '12 at 18:22