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Re: Left eigenvectors?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1034] Re: Left eigenvectors?
• From: Richard Mercer <richard at seuss.math.wright.edu>
• Date: Wed, 10 May 1995 06:25:29 -0400

>  Hi,
>  

>  I've been using Eigensystem[A] for a while now to find
>  the eigenvalues and eigenvectors of the matrix A. The
>  eigenvectors that it finds are the right eigenvectors of
>  A, i.e.,
>  

>    A.rvec == val*rvec,
>  

>  where val is an eigenvalue and rvec is the associated
>  right eigenvector.  I'd now like to find the left
>  eigenvectors of A, i.e.,
>  

>    lvec.A == val*lvec.
>  

>  How should I go about this?

The "left" eigenvectors of A are the same as the (right) eigenvectors of the  
transpose of A.
So just use 

Eigenvectors[Transpose[A]]

Richard Mercer