svd

A from-scratch favorite that probes linear algebra fluency. The signal is centering first, using SVD instead of forming the covariance matrix, and reading variance off the singular values. Here is the implementation and the details interviewers push on.

Dimensionality questions probe linear-algebra intuition and practical judgment together. What interviewers reward is what PCA really does (project onto max-variance directions), why high dimensions hurt, and the honest catch: it is unsupervised, so it can discard the exact direction your label needs. Here is the answer.