Estimated matrices intervening in |$\boldsymbol{\beta ^{\star }}$| for the matter power spectrum (left) and the matter PDF (right). The cross-covariance, covariance, and precision matrices are normalized i.e. we display |$\boldsymbol{D} ^{-1}\boldsymbol{\widehat{\Sigma }}\boldsymbol{D} ^{-1}$| with |$\boldsymbol{D} = \sqrt{\mathrm{diag}\left({\boldsymbol{\widehat{\Sigma }}}\right)}$|⁠. ‘od’ denotes the fractional overdensity bin |$\rho /\bar{\rho }$|⁠. For better visibility, the diverging colour scale is not forced to be centered at 0.0 for the |$\boldsymbol{\Sigma _{yc}}$| and |$\boldsymbol{\Sigma _{cc}}$| estimates in the upper left corner (power spectrum). All matrices are estimated using 500 simulation pairs, and represent the ‘close to optimal’ |$\boldsymbol{\beta ^{\star }}$| towards which the control matrix estimator tends in the multivariate setting.