[R] Spectral Decomposition [OOPS]

[(Ted Harding)]

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.

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Date: 29-Jun-07                                       Time: 14:42:19
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