How to calculate a 2D rotation vector with PCA?

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Hi all. I have two dataset (n x 2 matrix) in 2D space and I know their PCA matrices. PCA1 = [0.9981 -0.0622; 0.0622 0.9981], PCA2 = [0.5617 0.8273; 0.8273 -0.5617]
And I want to rotate one of these dataset and make them to be registered. How can I get a rotation vector?

Answers (1)

Alfonso Nieto-Castanon
Alfonso Nieto-Castanon on 23 May 2015
Edited: Alfonso Nieto-Castanon on 23 May 2015
find the angle between the first column of PCA1 and the first column of PCA2 (hint: cos(angle(a,b))*norm(a)*norm(b)=a'*b) and build your rotation matrix from that (e.g. [cos(ang) sin(ang); -sin(ang) cos(ang)])

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