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From: "Tian Lan" <lantian@mathworks.com>
Newsgroups: comp.soft-sys.matlab
Subject: Question about Matlab function eig
Date: Wed, 19 Dec 2007 22:04:30 +0000 (UTC)
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The eigen decomposition funcion eig in Matlab is supposed 
to return orthonormal vectors. Eg. given matrix A, we have 
V'AV=D. ideally, if the eigen vectors are authonormal to 
each other, we should have V'V=I, however, if you run the 
following command:

clc, A=rand(3,3), [V,D] = eig(A), V'*V,

You'll find this is not always true. The V'*V is not 
identity matrix. Also, for an asymmetric matrix A, we 
expect to get complex eigen value and eigen vectors. But 
if you run above command, you'll see it is not always true 
either. 

Can anyone explain this?