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Covariance-operator distance

{c}
{title2=$d_P$}

For factorizations $C_i=L_iL_i^*$, the Procrustes distance is $d_P(C_1,C_2)=\inf_R\lVert L_1-L_2R\rVert_{\mathrm{HS}}$, where $R$ ranges over unitary operators on the factor space. Equivalently,
$$
d_P(C_1,C_2)^2=\operatorname{tr}C_1+\operatorname{tr}C_2-2\operatorname{tr}\!\left((C_1^{1/2}C_2C_1^{1/2})^{1/2}\right).
$$


Procrustes distance between covariance operators

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 225 / 3 / b / Solution

Procrustes distance between covariance operators ( $d_{P}$ )

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