From: Jun Zhang (coolrainbow_at_yahoo.cn)
Date: Mon May 24 2010 - 06:48:34 CDT
I have one basic question about essential dynamics. It is well known that PCA performs such a calculation:
<(x-<x>)T (x-<x>)> = P lamda PT (where XT denotes the transpose of matrix X)
My question is , assume the coordination vector x(t), eigenvalue lambda1 and corresponding eigenvector P1,
1. what does it mean when we refer to "projection of the trajectory onto eigenvector P1", I think it is x(t)T*P1 (scalar production), is it true?
2. what does it mean when we refer to "projection of the structure onto eigenvector P1", which results a new structure? Can anyone give an explicit formula?
Thank you for your help!
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