Algorithm Mean center the data (optional) Compute the covariance matrix of the dimensions Find eigenvectors of covariance matrix Sort eigenvectors in decreasing order of eigenvalues Project onto eigenvectors in order Assume data matrix is of size For each dimension, compute mean Mean center by subtracting from each column to get Compute covariance matrix of size   If mean centered, Find eigenvectors and corresponding eigenvalues of Sort eigenvalues such that Project step-by-step onto the principal components , etc.