Singular Value - History

History

This concept was introduced by Erhard Schmidt in 1907. Schmidt called singular values "eigenvalues" at that time. The name "singular value" was first quoted by Smithies in 1937. In 1957, Allakhverdiev proved the following characterization of the nth s-number:

s_n(T) = \inf\big\{\, \|T-L\| : L\text{ is an operator of finite rank }<n \,\big\}.

This formulation made it possible to extend the notion of s-numbers to operators in Banach space.

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