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

1. ## 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

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

Thank you in advance!

2. ## 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))