Explain the role of eigenvalues and eigenvectors in PCA.

  • Eigenvalues represent direction, eigenvectors variance
  • Eigenvalues represent variance, eigenvectors direction
  • Neither plays a role in PCA
  • They are used in LDA, not PCA
In PCA, eigenvectors represent the directions in which the data varies the most, while the corresponding eigenvalues give the amount of variance in those directions. These are obtained from the covariance matrix of the original data, and the eigenvectors with the largest eigenvalues become the principal components that capture the most significant patterns in the data.
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