Re: Numerical Left Eigenvectors
- To: mathgroup at smc.vnet.net
- Subject: [mg6491] Re: [mg6369] Numerical Left Eigenvectors
- From: "Gordon A. Fox" <gfox at ucsd.edu>
- Date: Mon, 24 Mar 1997 21:38:45 -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