Can you discuss the geometric interpretation of Eigenvectors in PCA?

  • They align with the mean of the data
  • They define the direction of maximum variance
  • They define the scaling of the data
  • They represent clusters in the data
Geometrically, eigenvectors in PCA define the direction of maximum variance in the data. They are the axes along which the original data is projected, transforming it into a new coordinate system where variance is maximized.
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