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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