#4733: [with patch, needs review] matrix exponential for general matrices
----------------------------+-----------------------------------------------
Reporter: jason | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.2
Component: linear algebra | Resolution:
Keywords: |
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Comment (by wdj):
For my teaching, this is a very useful addition. However, the following
behavior seems odd. Maybe it is a quirk and not a bug. Still, I'd like
someone to comment on it before reviewing this further.
(It is based on the facts that exp(A) commutes with A
and the derivative of exp(At) equals Aexp(At)=exp(At)A.)
{{{
sage: t = var('t')
sage: A = matrix([[1,2],[3,4]])
sage: B = (t*A).exp()
sage: Bprime = matrix(map(diff,B.list()))
sage: B(1)*A == Bprime(1)
False
sage: B(1)*A == A*B(1)
False
sage: B*A == A*B
False
sage: MS = MatrixSpace(RR,2,2)
sage: MS(A*B(1)) == MS(Bprime(1))
False
sage: MS(A*B(1)); MS(Bprime(1))
[276.178649899715 402.884170665423]
[604.326255998134 880.504905897849]
[276.178649899715 402.884170665423]
[604.326255998134 880.504905897849]
sage: MS(A*B(-1)); MS(Bprime(-1))
[-0.405192443954626 0.196757133983140]
[ 0.295135700974710 -0.110056742979916]
[-0.405192443954626 0.196757133983140]
[ 0.295135700974710 -0.110056742979916]
sage: MS(A*B(-1)); MS(B(-1)*A)
[-0.405192443954626 0.196757133983140]
[ 0.295135700974710 -0.110056742979916]
[-0.405192443954626 0.196757133983140]
[ 0.295135700974711 -0.110056742979916]
sage:
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4733#comment:5>
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