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

 Messages: [ Previous | Next ]
 Kaba Posts: 289 Registered: 5/23/11
Re: Uniqueness of Q
Posted: Nov 7, 2012 12:38 PM

7.11.2012 18:01, Rupert wrote:
> 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.

>
> 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.

You are right, thanks. Are all solutions of this form?

--
http://kaba.hilvi.org

Date Subject Author
11/7/12 Kaba
11/7/12 Kaba
11/7/12 Rupert
11/7/12 Kaba
11/7/12 Kaba
11/7/12 quasi