vector

A vector is an element of a vector space, typically represented in practice as an ordered list (or array) of numbers. Vectors can represent points in a space, magnitudes with directions, or feature representations in an abstract mathematical space.

In AI and data science, data is commonly encoded as vectors, either as hand-engineered feature vectors or learned embeddings. With vectors, algorithms can compute similarities, distances, and gradients for learning.

Core operations on vectors include elementwise addition and scalar multiplication. Inner products (dot products) and norms determine angles and lengths, underpinning measures, such as cosine similarity and Euclidean distance.