The geometry of Euclidean space is founded on the familiar properties of length and angle. In Euclidean geometry, distance between points is measured by the length of the difference between the corresponding vectors, while angle relies on their dot product. The dot product is formalized by the more general concept of an inner product. Other types of inner product arise naturally in statistics, data analysis, and elsewhere. Each inner product has an associated norm, which is used to measure lengths of vectors. Inner products and norms lie at the heart of linear (and nonlinear) analysis, including machine learning.