I'm trying to show that the wanted matrix is $R = VU^T$, where $XY^T = UΣV^T$ is the singular value decomposition, but I'm having trouble understanding what it means or how to start.

  • $\begingroup$ What is your norm? Is it any natural norm? Also, RHS is square of Frobenius norm $||RX-Y||_F^2$. Maybe that can be helpful. $\endgroup$
    – Snowball
    May 16, 2021 at 10:49
  • $\begingroup$ Try to differentiate $tr((RX-Y)^\top(RX-Y))$ with respect to $R$. $\endgroup$
    – openspace
    May 16, 2021 at 11:12
  • $\begingroup$ @Snowball it is indeed a Frobenius norm, thanks for reminding me, I just don't understand what I need to do to "minimize" it. $\endgroup$
    – Mavi
    May 16, 2021 at 11:54
  • $\begingroup$ @Mavi you can check this problem: math.stackexchange.com/questions/946911/…. I think it answers your problem. $\endgroup$
    – Snowball
    May 16, 2021 at 12:36


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