juniorDimensionality Reduction
What are eigenvalues and eigenvectors in PCA?
Updated May 16, 2026
Short answer
Eigenvectors define directions of variance; eigenvalues define magnitude of variance.
Deep explanation
In PCA, eigenvectors of covariance matrix represent principal directions, while eigenvalues represent how much variance each direction explains.
Real-world example
Used in image compression to identify dominant patterns.
Common mistakes
- Confusing eigenvectors with original features.
Follow-up questions
- Why are eigenvectors orthogonal in PCA?
- What happens if eigenvalue is small?