\(\newcommand{\abs}[1]{\left\lvert#1\right\rvert} \newcommand{\restr}[2]{\left.#1\right\vert_{#2}} \newcommand{\der}{\operatorname{der}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\ad}{\operatorname{ad}} \newcommand{\Ad}{\operatorname{Ad}} \newcommand{\positiveset}{\mathbf{A}_+} \newcommand{\norm}[1]{\left\lVert #1 \right\rVert} \newcommand{\braket}[1]{\left\langle #1 \right\rangle} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)