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Kaba
Posts:
289
Registered:
5/23/11


Re: Uniqueness of Q
Posted:
Nov 7, 2012 12:43 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 >>> nonnegative 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.
Oops, take that back. The solution Q = UD'V^T needs to orthogonal, so all the elements in the diagonal of D' must be either +1 or 1. Anyway, are _these_ all solutions?
 http://kaba.hilvi.org



