Eigenfaces. Treat each face photo as one big vector (one number per pixel). PCA on many faces gives "eigenfaces" — the principal components, which look like ghostly face patterns. Any face becomes a weighted mix of a few eigenfaces. Cool, but PCA is sensitive to lighting and pose — because it can only see linear patterns.

The real limit: PCA finds the best straight line or flat plane. If your data actually curves — like a spiral — no flat surface fits it well, no matter how you rotate it.

Exam trap: "PCA finds any lower-dimensional structure" is false. Only linear structure. That's the whole reason Kernel PCA exists.