$$ \def\v{\boldsymbol} \def\m{\boldsymbol} \def\trans{^\mathsf{T}} \def\inv{^{-1}} \def\bmat{\begin{pmatrix}} \def\emat{\end{pmatrix}} \def\diag{\operatorname{diag}} \def\tr{\operatorname{tr}} \def\ad{\operatorname{ad}} \def\Ad{\operatorname{Ad}} \def\E{\operatorname{E}} \def\det#1{| #1 |} \def\her{^\mathsf{H}} \def\wed{\wedge} \def\given{\mid} \def\defeq{\triangleq} \def\Ys{{\cal Y}} \def\argmin{\mathop{\mathrm{argmin}}} \def\argmax{\mathop{\mathrm{argmax}}} \def\blockdiag{\mathop{\mathrm{blockdiag}}} \def\inner#1{\langle #1 \rangle} $$