[Scilab-users] Jordan normal form

[Samuel Gougeon]

Le 26/07/2020 à 19:13, fujimoto2005 a écrit :
> Dear Samuel,
>
> The following sample is from the sample 3 and 5 of wiki "Generalized
> eigenvector".
> https://en.wikipedia.org/wiki/Generalized_eigenvector#Example_3
>
> A=[[5 0 0 0]',[1 5 0 0]', [-2 2 5 0]', [4 2 3 4]']
> X=[[-14 4 -3 1]',[2 0 0 0]',[-2 2 0 0]',[0 0 1 0]']
> J=clean(inv(X)*A*X)
>
> J  =
>
>     4.   0.   0.   0.
>     0.   5.   1.   0.
>     0.   0.   5.   1.
>     0.   0.   0.   5.
>   
> J is a Jordan form.
>     
> [JJ,XX]=bdiag(A,1/%eps)
> XX  =
>
>     1.   0.   0.  -14.
>     0.   1.   0.   4.
>     0.   0.   1.  -3.
>     0.   0.   0.   1.
>
>   JJ  =
>
>     5.   1.  -2.   0.
>     0.   5.   2.   0.
>     0.   0.   5.   0.
>     0.   0.   0.   4.
>     
>   
>   JJ is a block dialog matrix but not a Jordan form,


OK. Switching the eigenvector and the subspace is OK, but in JJ(:,3), [0 
1 5] would be expected:
Beyond the block-diagonalization, the jordanization is actually not 
performed.

Quickly looking at the ATOMS/Linear algebra section does not clearly 
show resources connected to Jordan.
And there is no search engine on the Scilab forges...
Maybe as a utility in an external module?