       Re: Numerical Left Eigenvectors

• To: mathgroup at smc.vnet.net
• Subject: [mg6492] Re: [mg6369] Numerical Left Eigenvectors
• From: "Gordon A. Fox" <gfox at ucsd.edu>
• Date: Mon, 24 Mar 1997 21:38:47 -0500 (EST)
• Organization: University of California, San Diego
• Sender: owner-wri-mathgroup at wolfram.com

```seanross at worldnet.att.net wrote:
>
> Gregory Dwyer wrote:
> >
> > Greetings -
> >
> > When I use the "eigenvector" function to numerically calculate
> > eigenvectors, Mathematica seems to assume that I always want right
> > eigenvectors.  Is there some way to numerically calculate left eigenvectors?
> >
> > Thanks.
> >
> > Greg Dwyer.
> > Entomology, UMASS Amherst
> > dwyer at ent.umass.edu
>
> What is a left eigenvector?  The only eigenvectors I know of are ones
> that satisfy the following equation:
>
> Matrix . vector = constant vector.  Is this a right eigenvector?  Does
> left eigenvector mean
> vector. Matrix = constant vector?
>
> If so, have you looked for a way to express Matrix . column vector in
> terms of row vector . Matrix?  For a 2x2 case, it looks like
> Matrix.columnvector = rowvector.TransposeMatrix
>
> I am not sure how commutable square matrices and vectors are supposed to
> be.  Perhaps someone else out there with experience in something like
> group theory or who has a copy of MathTensor etc. could enlighten you
> further.

The left eigenvectors of the matrix A can be calculated as simply the
(right) eigenvectors of Transpose[A].

Cheers,
Gordon

```

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