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Rupert
Posts:
3,809
Registered:
12/6/04


Re: Uniqueness of Q
Posted:
Nov 7, 2012 11:01 AM


On Nov 7, 4:39 pm, Kaba <k...@nowhere.com> wrote: > 7.11.2012 17:30, Kaba wrote: > > Hi, > > > Let Q, U, D, V in R^{n x n}, where Q^T Q = U^T U = V^T V = I, and D is > > nonnegative diagonal. Consider the equation > > > Q^T UDV^T = VDU^T Q. > > > One solution to this equation is Q = UV^T. > > > Prove or disprove: this solution is unique. > > Disproved: Q = UV^T is also a solution. > > Prove or disprove: UV^T and UV^T are the only solutions. > > http://kaba.hilvi.org
Would it not be the case that any scalar multiple of UV^T is a solution?
Also I think UD'V^T is a solution whenever D' is diagonal.



