Date: Nov 7, 2012 12:38 PM
Author: Kaba
Subject: Re: Uniqueness of Q
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?

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