IX · Linear algebra
Norms & inner products
What it is
L1: |x|+|y|. L2: √(x²+y²). L∞: max(|x|, |y|). The geometry you choose determines which solutions are favoured.
Where it lives
Lasso (L1) vs Ridge (L2) regression, cosine similarity in embeddings, gradient-clipping by norm in deep learning.
The key insight
L1 produces sparse solutions (many zeros); L2 produces dense, smooth ones. Choosing a norm is choosing a prior — and it shows up everywhere from optimisation to crypto.