On the Early History of the Singular Value Decomposition
Copyright policy )On the Early History of the Singular Value Decomposition
The singular value decomposition is the factorization of a matrix \(A\) into the product \(U \sum V^ H\), where \(U\) is a unitary matrix, \(\sum\) a diagonal matrix, and \(V^ H\) another unitary matrix. The author surveys contributions of five mathematicians -- Eugenio Beltrami (1835-1899), Camille Jordan (1838-1921), James Joseph Sylvester (1814-1897), Erhard Schmidt (1876-1959), and Hermann Weyl (1885-1955) -- who were responsible for establishing the existence of the singular value decomposition and developing its theory. A brief history of subsequent developments is outlined, too. While Beltrami, Jordan, and Sylvester came to the decomposition through linear algebra, Schmidt and Weyl approached it from integral equations.
- University of Maryland, College Park United States
History of mathematics in the 20th century, Eigenvalues, singular values, and eigenvectors, Jordan, History of mathematics in the 19th century, Beltrami, Sylvester, History of linear algebra
History of mathematics in the 20th century, Eigenvalues, singular values, and eigenvectors, Jordan, History of mathematics in the 19th century, Beltrami, Sylvester, History of linear algebra
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