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\[
\begin{aligned}
Z_K &= \left[ z_K,P_{K-1}(z_K),P_{K-2}(P_{K-1}z_K), ..., P_1(P_2 \cdots P_{K-1}z_K) \right] \\ \\
\text{mit} \quad z_K &= (A + p_KI)^{-1}B, \\
\text{und} \quad P_K &= (A + p_kI)^{-1}(A - p_{k+1}I)\\ &= I - (p_{k+1} + p_k)(A + p_kI)^{-1}.
\end{aligned}
\]

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Text
{\scriptsize % damit der Unterschied besser sichtbar ist
\[ 
\begin{aligned} 
 Z_K &= \left[ z_K,P_{K-1}(z_K),P_{K-2}(P_{K-1}z_K), ..., P_1(P_2 \cdots P_{K-1}z_K) \right] \\ 
\text{mit} \quad z_K &= (A + p_KI)^{-1}B, \\ 
\text{und} \quad P_K &= (A + p_kI)^{-1}(A - p_{k+1}I)\\ &= I - (p_{k+1} + p_k)(A + p_kI)^{-1}.
\end{aligned} 
\]}
Text 
\end{document}