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Topic: Uniqueness of Q
Replies: 5   Last Post: Nov 7, 2012 1:20 PM

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Rupert

Posts: 3,809
Registered: 12/6/04
Re: Uniqueness of Q
Posted: Nov 7, 2012 11:01 AM
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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
> > non-negative 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.



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