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# Abstract symbolic matrix exponential 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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## Comments

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

## 1 Answer

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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 21:31:21 +0200

Seen: 434 times

Last updated: Mar 04 '15