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Math Help - Use of Trace in paper "Least-Squares Fitting of Two 3-D Point Sets"

  1. #1
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    Use of Trace in paper "Least-Squares Fitting of Two 3-D Point Sets"

    I'm reading the following paper:

    "Least-Squares Fitting of Two 3-D Point Sets"
    by Arun, Huang, and Bolstein
    IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 9, No. 5, September 1987, pages 698-700

    link: http://www.google.com/url?sa=t&rct=j...PNelCS9sTejndw

    I can't understand the equation 14 of this paper, where Trace is used.

    Thank you in advance!
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  2. #2
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    Re: Use of Trace in paper "Least-Squares Fitting of Two 3-D Point Sets"

    I think I understood it.

    sum(qi'T*R*qi) = sum(Trace(qi'T*R*qi)) = sum(Trace(Rqiqi'T)) = Trace(sum(Rqiqi'T))
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