$$ \newcommand{\R}{\mathbb{R}} \newcommand{\SSS}{\mathbb{S}} \newcommand{\E}{\mathbb{E}} \newcommand{\C}{\mathbb{C}} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\dist}{\mathrm{dist}} \newcommand{\span}{\mathrm{Span}} \newcommand{\diag}[1]{\mathrm{diag}(#1)} \newcommand{\dim}[1]{\mathrm{dim} \, #1} \newcommand{\tr}[1]{\mathrm{tr}(#1)} \newcommand{\partder}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\rank}[1]{\mathrm{rank} \, #1} \newcommand{\inner}[1]{\langle #1 \rangle} \newcommand{\innerbig}[1]{\left \langle #1 \right \rangle} \newcommand{\abs}[1]{\lvert #1 \rvert} \newcommand{\norm}[1]{\lVert #1 \rVert} \newcommand{\ker}[1]{\text{ker}(#1)} \newcommand{\supp}[1]{\text{supp}(#1)} \newcommand{\calA}{\mathcal{A}} \newcommand{\calB}{\mathcal{B}} \newcommand{\calC}{\mathcal{C}} \newcommand{\calD}{\mathcal{D}} \newcommand{\calE}{\mathcal{E}} \newcommand{\calF}{\mathcal{F}} \newcommand{\calG}{\mathcal{G}} \newcommand{\calH}{\mathcal{H}} \newcommand{\calI}{\mathcal{I}} \newcommand{\calJ}{\mathcal{J}} \newcommand{\calK}{\mathcal{K}} \newcommand{\calL}{\mathcal{L}} \newcommand{\calM}{\mathcal{M}} \newcommand{\calN}{\mathcal{N}} \newcommand{\calO}{\mathcal{O}} \newcommand{\calP}{\mathcal{P}} \newcommand{\calQ}{\mathcal{Q}} \newcommand{\calR}{\mathcal{R}} \newcommand{\calS}{\mathcal{S}} \newcommand{\calT}{\mathcal{T}} \newcommand{\calU}{\mathcal{U}} \newcommand{\calV}{\mathcal{V}} \newcommand{\calW}{\mathcal{W}} \newcommand{\calX}{\mathcal{X}} \newcommand{\calY}{\mathcal{Y}} \newcommand{\calZ}{\mathcal{Z}} \newcommand{\bh} \newcommand{\bf} \newcommand{\Pker}{P_{\ker{L}^{\perp}}} $$