Vectors
A vector is an arrow. That simple idea — something with a direction and a size — is the foundation of everything from image recognition to language models. This topic builds geometric intuition first, notation second.
What Is a Vector?
Vectors are the atoms of machine learning. Before neural networks, embeddings, or matrix operations make sense, you need a solid geometric and algebraic feel for what a vector actually is.
Vector Operations
Three arithmetic operations on vectors — addition, scalar multiplication, and the dot product — appear constantly in machine learning. This chapter builds geometric intuition for each and shows how the dot product leads directly to cosine similarity, the comparison metric at the heart of embedding search.
Vector Spaces and Basis
Every vector lives in a vector space — a structured arena where addition and scaling are always valid. The choice of basis for that space determines how vectors are described as lists of numbers. Understanding why a basis must be linearly independent, and what it means for vectors to span a space, provides the geometric foundation for making sense of why ML models learn in hundreds of dimensions.