Date: Nov 7, 2012 10:39 AM Author: Kaba Subject: Re: Uniqueness of Q 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.

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