\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{cd}
\begin{document}
\[
\begin{tikzcd}
\left< x, y \right>
\ar[r, "{{\left( \begin{array}{cc} a & b \\ c & d \end{array} \right)}}"]
&
\left< z,w \right>
\\
\end{tikzcd}
\]
\end{document}
generates the error message
Undefined control sequence.
\pgf@let@token ...{{\left ( \begin {array}{cc} a &
b \\ c & d \end {array} \...
The problem is discussed in section 3.4 of the tikzcd manual at http://ctan.math.washington.edu/tex-archive/graphics/pgf/contrib/tikz-cd/tikz-cd-doc.pdf. One solution is as follows: use the "ampersand replacement" option to tikzcd to use a different character for separating nodes in the commutative diagram. This leaves the ampersand available for use in the array in the arrow's label.
\documentclass{amsart}
\usepackage{tikz}
\usetikzlibrary{cd}
\begin{document}
\[
\begin{tikzcd}[ampersand replacement=\&]
\left< x, y \right>
\ar[r, "{{\left( \begin{array}{cc} a & b \\ c & d \end{array} \right)}}"]
\& %% Note replacement of & by \& here
\left< z,w \right>
\\
\end{tikzcd}
\]
\end{document}
\documentclasscommand, include any necessary packages and be as small as possible to demonstrate your problem. Ideally it should compile unless, of course, that is what you are asking about. – Andrew Jul 18 '17 at 23:39