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Abstract symbolic matrix exponential

asked 2015-03-04 14:31:21 -0500

anonymous user

Anonymous

I'm new to Sage. I was told Sage can do something way better than Mathematica. I tried and didn't see the magic. So I was wondering if I did wrong.

My goal: to compute matrix exponential of 2x2 matrix whose elements are a function of time.

A(t)=[[-a(t), a(t)],[b(t), -b(t)]]

B(s)=integrate of A(t) from 0 to s

exp(B(s)) ===> I was told this can be done in one step like treating B as a constant matrix exp(B*t)

Is this possible? My approach is to solve a system of differential equations.

Thanks.

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Are a(t) an b(t) known ? Of which form ? Could you please give more details and a concrete example ?

tmonteil gravatar imagetmonteil ( 2015-03-04 14:57:11 -0500 )edit

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answered 2017-05-22 07:36:46 -0500

t, s = var(' t s ')

A = matrix([[3*t,t^2],[-2*t, t]])

B = A.apply_map(lambda e: integrate(e,t,0,s))

B.exp()

I Think this is what you are looking for. Note that simple 'integrate' function won't integrate the matrix.

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Asked: 2015-03-04 14:31:21 -0500

Seen: 361 times

Last updated: Mar 04 '15