How I can use the eig function for nonsymmetric matrices?
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Traian Preda
il 7 Ago 2014
Modificato: Chris Turnes
il 7 Ago 2014
Hi,
I have a non symmetric matrix and I try to figure out which option of the eig I should use? Thank you
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Chris Turnes
il 7 Ago 2014
The eig function does not require any additional options for nonsymmetric matrices. There is an example of this in the documentation for eig:
>> A = gallery('circul',3)
A =
1 2 3
3 1 2
2 3 1
>> [V,D] = eig(A);
>> V\A*V % verify that V diagonalizes A
ans =
6.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i
-0.0000 - 0.0000i -1.5000 + 0.8660i -0.0000 - 0.0000i
-0.0000 + 0.0000i -0.0000 + 0.0000i -1.5000 - 0.8660i
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Chris Turnes
il 7 Ago 2014
Modificato: Chris Turnes
il 7 Ago 2014
How are you trying to rebuild the matrix from the eigendecomposition? Note that since the matrix is not symmetric, it is not true that V^{-1} = V^H. Therefore, to reconstruct the matrix, you should instead try
>> Ar = V*D/V; % Ar = V*D*V^{-1}
which is the proper eigendecomposition. When I try this with the matrix you posted, I get:
>> Ar = V*D/V; % Ar = V*D*V^{-1}
>> norm(a - Ar)
ans =
2.4546e-15
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