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MathGroup Archive 1997

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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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