Vector Norms

You've measured a vector's length with √(x² + y²) — the Euclidean, or L2, norm. But it's not the only way. Add the absolute components and you get the L1 norm (Manhattan distance — how a taxi drives on a grid). Take the largest component and you get L∞. Each norm measures 'size' differently, and the choice changes what 'sparse', 'close', and 'robust' mean — driving LASSO regression, compressed sensing, and deep-learning regularization.