Schematic representation of PCA applied on LBL RVs. The number of dimensions of the space is equal to the number of observations (here two for ease of visualisation), while each element of the data cloud is made of one LBL RV time-series RV_i(t). The Doppler shift RV_DS (black arrow), which defines the barycentre of the cloud, is equal to a planetary signal RV_P (blue arrow) plus a mean systematic effect V₁ (red arrow). Because PCA is mean-invariant, the first PC will be along the V₁(t) direction and can be used to correct the RVi(t).