Applying Linear Algebra to Functions: Functions as Vectors

Functions as Vectors are often first introduced as lists of real numbers—i.e. the familiar notation we use for points, directions, and more.

This article received an honorable mention in 3Blue1Brown’s Summer of Math Exposition 3!

Conceptualizing functions as infinite-dimensional vectors lets us apply the tools of linear algebra to a vast landscape of new problems, from image and geometry processing to curve fitting, light transport, and machine learning.