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I'm having a little trouble understanding the meaning behind the Jacobian of an SVD. I understand what the Jacobian is, but I don't see how you can derive a Jacobian from the SVD. To me, the SVD is just USV_transpose - I don't see how a matrix can be differentiated, since they don't really seem to be functions of anything.

http://www.ics.forth.gr/_publications/2000_eccv_SVD_jacobian.pdf

I've been looking at the above pdf just to get a better understanding, but equation (7) (the differentiation of the singular values) is really where I get lost.

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