# How can i calculate e^A*t

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How can i calculate e^A*t without using Markov Chain?

Where e=exp , A is a square matrix, and t is a variable

##### 10 Comments

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### More Answers (5)

Kye Taylor
on 31 May 2012

Use the expm function for computing a matrix exponential

##### 4 Comments

Walter Roberson
on 9 Nov 2017

We tried a number of times to get the original poster to clarify, but all we got was that they want the exp() solution and that they are looking for a "deeper reason" for something. The poster effectively defined the exp() solution as being the correct one.

Your analysis might well be what the poster really needed, but it is contrary to what little they defined as being correct for their needs.

Shenhai
on 20 Jan 2017

Edited: Shenhai
on 20 Jan 2017

I guess it is not always possible to get the close form solution of exp(At)...

Sometimes I can get result with: exp(At) = iL(sI-A)^-1, where iL is the inverse Laplace transformation, like:

syms s t

A = [0 1;0 0];

expAt = ilaplace(inv(s*eye(size(A,1))-A),s,t);

This will give the result as: [1 t;0 1]

Any other ideas?

##### 0 Comments

Shahram Bekhrad
on 8 Jun 2012

##### 0 Comments

ABCD
on 29 Sep 2016

Dear Nick, do you mean this?

>> a = [1 2 3 ; 2 5 2; 1 4 3]

a =

1 2 3

2 5 2

1 4 3

>> syms t >> exp(a*t)

ans =

[ exp(t), exp(2*t), exp(3*t)] [ exp(2*t), exp(5*t), exp(2*t)] [ exp(t), exp(4*t), exp(3*t)]

##### 1 Comment

ABCD
on 29 Sep 2016

>> a = [1 2 3 ; 2 5 2; 1 4 3]

a =

1 2 3

2 5 2

1 4 3

>> syms t

>> exp(a*t)

ans =

[ exp(t), exp(2*t), exp(3*t)]

[ exp(2*t), exp(5*t), exp(2*t)]

[ exp(t), exp(4*t), exp(3*t)]

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