Vector

A vector is an ordered array of numbers that represents data as a point in multi-dimensional space, serving as the fundamental representation format for modern AI systems. In machine learning, features extracted from raw inputs like text, images, and audio are converted into numerical vectors that algorithms can process. Word embeddings represent words as dense vectors where semantic relationships are captured through spatial proximity, so similar concepts cluster together. Neural networks transform input vectors through successive layers of matrix operations, progressively extracting higher-level features. In the context of vector databases and semantic search, vectors enable similarity comparisons through distance metrics like cosine similarity and Euclidean distance. The dimensionality of vectors varies widely, from small feature vectors with tens of dimensions to large language model embeddings with thousands of dimensions.