Eigendecomposition

pca is the linear algebra exam question that escaped into industry. given a cloud of points in \(\mathbb{R}^d\), it finds the orthogonal directions along which the cloud spreads the most, and lets you throw away the rest. 𐃏 two apparently different questions — “which directions carry the most variance?” and “which subspace loses the least when i project onto it?” — turn out to have the same answer, and that answer is an eigendecomposition.