= Population principal component
{title2=$Y_j=q_j^T(X-\mu),\quad\Sigma q_j=\lambda_jq_j$}
The <population principal components> are centered linear compounds along an orthonormal eigenbasis of the <covariance matrix>, ordered by decreasing <eigenvalue>. They are uncorrelated and have <variances> $\lambda_j$. Each successive direction maximizes <variance> subject to unit length and orthogonality to earlier directions. Uncorrelatedness does not imply <independence> unless additional distributional assumptions hold.
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