Singular Value Decomposition

Singular Value Decomposition (SVD) is a fundamental matrix factorization technique that decomposes any m × n matrix A into the product A = U Σ V^T, where U and V are orthogonal matrices and Σ is a diagonal matrix of singular values. Developed by Gene Golub and others in the 1960s–1970s, SVD is the most robust method for analyzing matrix structure and solving linear systems.