Editing Proper orthogonal decomposition (section)

== POD and PCA ==
The main use of POD is to '''decompose''' a physical field (like pressure, temperature in fluid dynamics or stress and deformation in structural analysis), depending on the different variables that influence its physical behaviors. As its name hints, it's operating an Orthogonal Decomposition along with the Principal Components of the field. As such it is assimilated with the [[principal component analysis]] from [[Karl Pearson|Pearson]] in the field of statistics, or the [[singular value decomposition]] in linear algebra because it refers to [[eigenvalues and eigenvectors]] of a physical field. In those domains, it is associated with the research of Karhunen<ref>{{Cite book|last=Karhunen|first=Kari|title=Zur spektral theorie stochasticher prozesse|year=1946}}</ref> and Loève,<ref>{{Cite journal|last1=David|first1=F. N.|last2=Loeve|first2=M.|date=December 1955|title=Probability Theory.|url=http://dx.doi.org/10.2307/2333409|journal=Biometrika|volume=42|issue=3/4|pages=540|doi=10.2307/2333409|jstor=2333409|issn=0006-3444|url-access=subscription}}</ref> and their [[Karhunen–Loève theorem]].