UP
$$ \newcommand{\RR}{\mathbb{R}} \newcommand{\PP}{\mathbb{P}} \newcommand{\NN}{\mathbb{N}} \newcommand{\ZZ}{\mathbb{Z}} \newcommand{\CC}{\mathbb{C}} \newcommand{\HH}{\mathbb{H}} \newcommand{\alg}[1]{\mathfrak{#1}} \newcommand{\mat}[1]{ \begin{pmatrix} #1 \end{pmatrix} } \renewcommand{\bar}{\overline} \renewcommand{\hat}{\widehat} \renewcommand{\tilde}{\widetilde} \newcommand{\inv}[1]{ {#1}^{-1} } \newcommand{\block}[1]{\left(#1\right)} \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\trace}[1]{\mathrm{tr}\block{#1}} \newcommand{\norm}[1]{ \left\| #1 \right\| } \newcommand{\argmin}[1]{ \underset{#1}{\mathrm{argmin}} } \newcommand{\argmax}[1]{ \underset{#1}{\mathrm{argmax}} } \newcommand{\st}{\ \mathrm{s.t.}\ } \newcommand{\sign}[1]{\mathrm{sign}\block{#1}} \newcommand{\half}{\frac{1}{2}} \newcommand{\inner}[2]{ \langle #1, #2 \rangle } \newcommand{\dd}{\mathrm{d}} \newcommand{\ddd}[2]{\frac{\partial #1}{\partial #2} } \newcommand{\db}{\dd^b} \newcommand{\ds}{\dd^s} \newcommand{\dL}{\dd_L} \newcommand{\dR}{\dd_R} \newcommand{\Ad}{\mathrm{Ad}} \newcommand{\ad}{\mathrm{ad}} \newcommand{\LL}{\mathcal{L}} \newcommand{\Krylov}{\mathcal{K}} \newcommand{\diag}{\mathrm{diag}} \newcommand{\tr}{\mathrm{tr}} \newcommand{\sinc}{\mathrm{sinc}} $$

Research Notes

yo euclid

These are random research notes, generally providing quick reference on recurring mathematical issues. Hopefully they can be helpful to others :)