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

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Kaba

Posts: 289
Registered: 5/23/11
Re: Uniqueness of Q
Posted: Nov 7, 2012 10:39 AM
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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



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