Inner product

An inner product is a mathematical operation that measures the similarity or angle between two vectors, which can be thought of as arrows pointing in space. It produces a single number, called a scalar, reflecting how much the two vectors point in the same direction. If the inner product is large and positive, the vectors are closely aligned; if it’s zero, they are perpendicular; and if negative, they point in opposite directions. Inner products are fundamental in fields like geometry, physics, and machine learning, helping quantify relationships and structure within data.