𝑪𝑪 is a 𝑛𝑛 × 𝑛𝑛 matrix, the covariance matrix: The standardized 𝑍𝑍 𝑖𝑖 (centered at 0 and scaled by forcing its variation to 1) now replaces 𝑋𝑋 𝑖𝑖 in Eqs. ( )-( ) so that the PCA is not biased in any chemical element 𝑖𝑖 with high absolute magnitude in 𝑋𝑋 𝑖𝑖 . To keep the coefficients in principal components 𝒗𝒗 orthonormal, the components 𝐶𝐶 𝑖𝑖 in 𝒗𝒗 are rescaled by the standard deviation of the corresponding 𝑋𝑋 𝑖𝑖 ,