Editing Singular value (section)

== 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, Allahverdiev proved the following characterization of the ''n''th singular number:<ref>[[Israel Gohberg|I. C. Gohberg]] and [[Mark Krein|M. G. Krein]]. Introduction to the Theory of Linear Non-selfadjoint Operators. American Mathematical Society, Providence, R.I.,1969. Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18.</ref> 
: <math>\sigma_n(T) = \inf\big\{\, \|T-L\| : L\text{ is an operator of finite rank }<n \,\big\}.</math>

This formulation made it possible to extend the notion of singular values to operators in [[Banach space]]. 
Note that there is a more general concept of ''[[s-numbers]]'', which also includes Gelfand and Kolmogorov width.