Editing Matrix decomposition (section)

=== Algebraic polar decomposition ===
*Applicable to: square, complex, non-singular matrix ''A''.<ref>{{harvnb|Choudhury|Horn|1987|pp=219–225}}</ref>
*Decomposition: <math>A=QS</math>, where ''Q'' is a complex orthogonal matrix and ''S'' is complex symmetric matrix.
*Uniqueness: If <math>A^\mathsf{T}A</math> has no negative real eigenvalues, then the decomposition is unique.<ref name=":0">{{Cite journal|last=Bhatia|first=Rajendra|date=2013-11-15|title=The bipolar decomposition|journal=Linear Algebra and Its Applications|volume=439|issue=10|pages=3031–3037|doi=10.1016/j.laa.2013.09.006|doi-access=}}</ref>
*Comment: The existence of this decomposition is equivalent to <math>AA^\mathsf{T}</math> being similar to <math>A^\mathsf{T}A</math>.<ref>{{harvnb|Horn|Merino|1995|pp=43–92}}</ref>
*Comment: A variant of this decomposition is <math>A=RC</math>, where ''R'' is a real matrix and ''C'' is a [[circular matrix]].<ref name=":0" />