Re: Understanding eig()

[Rich Shepard]

On Sun, 1 Aug 2004, Henry F. Mollet wrote:

> In the real world we need real solutions but there are exceptions.  I assume
> that GNU Octave lists the eigenvalues in the order of the absolute value
> octave:3> la=diag(la)
> la =
>
>    11.72374 +  0.00000i
>    -1.05925 +  5.81855i
>    -1.05925 -  5.81855i
>    -0.00571 +  2.32593i
>    -0.00571 -  2.32593i
>    -2.03018 +  0.00000i
>     0.21818 +  0.82953i
>     0.21818 -  0.82953i

Henry,

  Then my assumption that what octave produced as a result of the eig()
function is a list of the eigenvalues, in rank order, is correct. That's
good to know. Many thanks.

> octave:8> w1=abs(w(:,imax))
> w1 =
>
>   0.083462
>   0.371274
>   0.337533
>   0.033013
>   0.511678
>   0.537519
>   0.348685
>   0.260477
> % Right eivenvector associated with la1 is also real.

  Aha! Guess it's been too many years since my linear algebra class. :-)

> In my field, matrices are classified as follows:
> Nonnegative
> Reducible vs. irreducible
> If irreducible, primitive vs. imprimitive
> (after Caswell 2001, Matrix Population Models p. 85).

  Well, I've not done population modeling for about 30 years now. The
closest I've come to mathematics in my field of environmental risk
management is statistics (numerical and spatial).

  I'm getting a better sense of how to use octave, but still have a long way
to go. But, I'll put the request for explanation of an error message in a
separate post.

Again, thanks,

Rich

-- 
Dr. Richard B. Shepard, President
Applied Ecosystem Services, Inc. (TM)
<http://www.appl-ecosys.com>



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