Generalized eigenvectors not orthogonal
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I use eig to solve a generalized eigenvalues problem from two symmetric real matrices and resulting eigenvalues are not orthogonal even though there is no degeneration in the eigenvalues. Minimal code to reproduce this:
A=randn(10); B=randn(10);
A=A+A'; B=B+B';
[V,D]=eig(A,B);
diag(D)
V(:,1:6)'*V(:,1:6)
What do I miss?
1 Comment
Matt J
on 21 Nov 2014
I'm not aware of any result saying they should be orthogonal. The material here
mentions they will be B-orthogonal, but only if B is positive definite.
Answers (1)
MA
on 21 Nov 2014
They are orthogonal, what is the problem?
clear all
close all
clc;
A=randn(10);
B=randn(10);
AA=A+A';
BB=B+B';
[V,D]=eig(AA);
[VV,DD]=eig(BB);
diag(D);
diag(DD);
V(:,1:10)'*V(:,1:10)
VV(:,1:10)'*VV(:,1:10)
2 Comments
MA
on 21 Nov 2014
in your case must be x=y:
clear all
clc;
A=randn(10);
B=randn(10);
AA=A+A';
BB=B+B';
[V,D]=eig(AA,BB);
%x=y
x=AA*V
y=BB*V*D
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