Computing the Singular Value Decomposition (SVD) is a key problem in linear algebra, and is incredibly useful in a wide variety of contexts in machine learning, statistics, signal processing, and other fields. Formally, the SVD of a real m × n matrix A is a factorization of the form A = U Σ Vᵀ, where U is an m × m orthogonal matrix of left singular vectors, Σ is an m × n diagonal matrix of singular values, and Vᵀ is an n × n orthogonal matrix of right singular vectors.