[Eeglablist] Eigenvectors, reflections and SVD
marco.congedo at irisa.fr
Wed Dec 8 02:19:36 PST 2004
I have a question on Eigenvectors, reflection and SVD.
Given a square non-symmetric matrix A, consider the Singular Value
Decomposition (SVD) of its symmetric part B=1/2(A+A'), as
U and V, both orthogonal, should now be equal, hence projecting
in the same space. However I noticed that V
have some rows with sign reversed as compared to U.
It seems that the spaces for the U' projection and V' projection
are identical, out of a reflection of one or more axes.
My question is, is there some information in this "reflection" and if so
what it means, or it is just an artifact of the SVD algorithm?
Thank you very much.
Marco Congedo, PhD
SIAMES Project, IRISA
Campus de BeauLieu
35042 Rennes France
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