Consider this minimal example :
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\begin{document}
\begin{alignat}{2}
&\frac{1}{2} log(\langle d_x, d_x \rangle + \frac{1}{2} log(\langle d_y, d_y \rangle - \log(\langle d_x, d_y \rangle) &> 0 \quad| \cdot 2 \\\nonumber
\Leftrightarrow \quad &log(\langle d_x, d_x \rangle + log(\langle d_y, d_y \rangle - 2 \log(\langle d_x, d_y \rangle) &> 0 \\\nonumber
\Leftrightarrow \quad &log(\langle d_x, d_x \rangle + log(\langle d_y, d_y \rangle &> 2 \log(\langle d_x, d_y \rangle) \\\nonumber
\Leftrightarrow \quad &e^{log(\langle d_x, d_x \rangle + log(\langle d_y, d_y \rangle} &> e^{2 \log(\langle d_x, d_y \rangle)} \\\nonumber
\end{alignat}
\end{document}
I expect the start of the line as well as the > sign to be aligned. However only the start of the line is aligned and not the > sign. See this:

