# I have matrix A and I need to find (e^(At)) where t is the sampling time. How to find that? Also what is the difference between exp(A) and expm(A)?

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VARSHA J LAL on 20 Oct 2021
Commented: VARSHA J LAL on 22 Oct 2021
How to find (e^(At)) that? Also what is the difference between exp(A) and expm(A)?

James Tursa on 20 Oct 2021
Edited: James Tursa on 20 Oct 2021
exp(A) just takes the exp( ) of the scalar elements individually. I.e., exp(A(1,1)), exp(A(1,2)), etc.
expm(A) takes the matrix exponential. I.e., conceptually the equivalent of eye(n) + A + A^2/2! + A^3/3! + ...
These are two very different operations. From your description it looks like you should be using expm( ).
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VARSHA J LAL on 22 Oct 2021
thank you @James Tursa

### More Answers (2)

KSSV on 20 Oct 2021
A = rand(2) ;
t = linspace(0,1) ;
iwant = zeros(2,2,100) ;
for i = 1:100
iwant(:,:,i) = exp(A*(t(i))) ;
end
exp might give less accurate values for [0,1]; in that case expm will be accurate

Bruno Luong on 20 Oct 2021
Edited: Bruno Luong on 20 Oct 2021
Math notation e^(At) is computed in MATLAB with
expm(A*t)
or equivalently
expm(A)^t

R2017a

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