Monday, 16 July 2018

svd - How to find the Takagi decomposition of a symmetric (unitary) matrix?

The Takagi decomposition is a special case of the singular value decomposition for symmetric matrices. More exactly:





Let U be a symmetric matrix, then Takagi tells us there is a unitary
V such that U=VDVT (with D>0 diagonal).




My question is basically: how to construct this V? Preferably I am looking for the `easiest'/most straight-forward way (which probably won't be the most efficient way!)



Note: For the case I am interested in, U is in fact unitary (in which case Takagi gives U=VVT). I'm happy to specialize to that special case if that makes the algorithm easier.

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