Linear Combinations

A kitchen stocks two base recipes. By choosing how much of each to use, a chef produces a whole menu of dishes — each dish is a weighted mix of the two originals. Linear algebra does the same with vectors: take two arrows, pick two numbers, and c₁v₁ + c₂v₂ produces a brand-new arrow. This one operation — the linear combination — is the atom of the entire field, and of every neural network layer.