Each square matrix possesses a collection of one or more distinguished scalars, called eigenvalues, each associated with certain distinguished vectors known as eigenvectors. From a geometrical viewpoint, when the matrix acts on vectors via matrix multiplication, the eigenvectors specify the directions of pure scaling and the eigenvalues the extent the eigenvector is scaled. Eigenvalues and eigenvectors are of absolutely fundamental importance, and assume an essential role in a broad range of applications, including machine learning and data analysis, dynamical systems, both continuous and discrete, statistics, and many more.