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)?

How to find (e^(At)) that? Also what is the difference between exp(A) and expm(A)?

Answer 1

[James Tursa]

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( ).

[VARSHA J LAL]

thank you @James Tursa

Answer 2

[KSSV]

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

Answer 3

[Bruno Luong]

Math notation e^(At) is computed in MATLAB with

expm(A*t)

or equivalently

expm(A)^t