Hi All,

Suppose I've a symmetric matrix $A_{N \times N} = (A_{ij})$ which has a eigen value decomposition $A = UDU'$. I would like to know under what conditions $\frac{\partial U}{\partial A_{ij}}$ exists for all $i,j = 1,2, \ldots, N$. I found the following paper which talks about estimating the Jacobian of the SVD transformation

http://www.ics.forth.gr/cvrl/publications/conferences/2000_eccv_SVD_jacobian.pdf

But its not very clear regarding the conditions that the matrix $A$ would need to satisfy. Any help is much appreciated.

Thanks Ashin