Correlation matrices for the properties of haloes with the lowest masses considered here, 5·10¹¹<M_h (M_⊙ h⁻¹)<7·10¹¹. Each matrix element is colour coded with the value of the Spearman rank correlation value, from −1 to 1, as indicated in the colour bar. We distinguish between intrinsic halo properties, c={c_vir, λ, c/a, b/a}, and environmental ones, α={b₁, α_4R, δ_10R}. We can understand these correlation matrices as being composed of four blocks (Eq. (4)): correlations between environmental properties, ρ_αα; correlations between intrinsic and environmental properties, ρ_αc and ρ_cα; and correlations between intrinsic halo properties, ρ_cc. The LR simulation matrix is at the top, outlined in grey, and the HR one is at the bottom, outlined in black. Since the environmental properties are well resolved in both simulations, we indicate a common correlation block matrix, ρ_αα. Correlations between different halo properties are affected by resolution effects, as can be seen by comparing the top LR matrix with the bottom HR one. The key idea of our method is to incorporate the missing correlations, i.e. the shades of blue, which indicate negative correlations present in the HR simulation (bottom matrix) but not in the LR simulation (top matrix).