Thank you very much, for the useful information !
Where can I find a complete and good documentation about Sage, better
then the tutorial or the reference ?
Thank you again.
On Mar 10, 8:00 pm, Jason Grout <jason-s...@creativetrax.com> wrote:
> alex wrote:
> > This seems to work:
> > given a symbolic matrix P of dimension 2x2 do:
>
> > EVECP = maxima(P).eigenvectors()
> > EVEC1 = EVECP.part(2)
> > (first eigenvector)
> > EVEC2 = EVECP.part(3)
> > (second eigenvector)
> > EIGENVECT = (matrix(SR, 2,2, [EVEC1.sage(), EVEC2.sage()])).transpose
> > () (matrix of eigenvectors)
>
> > for the inverse:
> > EIGENVECTINV = EIGENVECT.inverse()
> > (EIGENVECTINV * EIGENVECT).simplify_rational()
> > gives identity matrix.
>
> > the eigenvalues of P with multiplicity (!) can be read with
> > EVECP.part(1)
>
> > Is this correct ?
>
> > Is there a way to symbolically compute the matrix exponential
> > directly ?
> > THX !
>
> There should be a matrix exponential function:
>
> sage: var('a,b,c,d')
> (a, b, c, d)
> sage: A=matrix([[a,0],[0,d]])
> sage: A.exp()
>
> [e^a 0]
> [ 0 e^d]
> sage: A=matrix([[a,2],[0,d]])
> sage: A.exp()
>
> [ e^a (2*e^d - 2*e^a)/(d - a)]
> [ 0 e^d]
>
> Jason
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