On 29-Jun-07 13:23:05, Ted Harding wrote: > [Sorry -- a silly typo in my previous]: > If A is not symmetric, you have "left" eigenvectors: > > x'*A = lambda*x' > > and "right" eigenvectors: > > A*x = lambda*x > > and the "left" eigenvectors are not the same as the "right" > eigenvectors, though you have the same set of eigenvalues lambda > in each case. > > You then have > > A = L'*B*R
Should be: A = R*B*L' in that L'*R = I (unit), so then A*R = R*B so each column (right eigenvector) of R is multiplied by the corresponding lambda; L'*A = B*L' so each row (left eigenvector) of L' is multiplied by the corresponding lambda. Apologies for the slip! Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[EMAIL PROTECTED]> Fax-to-email: +44 (0)870 094 0861 Date: 29-Jun-07 Time: 14:42:19 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
