G.W. Stewart's 1993 SIAM Review paper reconstructs the singular value decomposition's development across five decades of linear algebra. The survey identifies Eugenio Beltrami and Camille Jordan as independent discoverers of the core theorem in the 1870s, though their work on bilinear forms went unrecognized as a general matrix factorization. Erhard Schmidt and Hermann Weyl later extended the result to integral operators and infinite dimensions in the early 1900s, framing it as spectral theory for compact operators.

The paper documents how Golub and Kahan's 1965 bidiagonalization algorithm and Golub and Reinsch's 1970 QR-based implementation made SVD numerically stable for digital computers. Stewart highlights Gene Golab's role in recognizing SVD as a computational tool rather than purely theoretical construct. The 1971 LINPACK inclusion cemented its status in scientific computing.

Stewart argues the decomposition's delayed adoption stemmed from notational fragmentation — Beltrami used geometric language, Schmidt functional analysis, and early numerical analysts treated it as a least-squares subroutine. The 1993 survey unified these threads, establishing SVD as the canonical rank-revealing factorization underlying principal component analysis, latent semantic indexing, and modern recommender systems.