MATLAB: How can i calculate e^A*t

exponentialhumourmarkovmatrix

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

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

Best Answer

exp(A.*t)

Related Solutions

MATLAB: Why exp(at) is not equal to ilaplace ((si-a)^-1) in matlab

The matrix exponential e^At = L^-1 {(sI-A)^-1}

This does not mean you can just take exp of each of the elements of the matrix.

This is wrong

Matrix exponential:
e^(At) =/= exp(A*t) = [ exp(-3*t), exp(-t) ; exp(2*t), 1]

MATLAB does element wise operation of matrices hence you can't compute the matrix exponential by the above method.

Maybe this will give you a better idea of how it is defined:

http://en.wikipedia.org/wiki/Matrix_exponential#via_Laplace_transform

MATLAB: Code for plot figure

lamda=0.2;
mu=1-lamda;
P1=mu^2/(mu+lamda)^2;
P2=2*lamda*mu/(mu+lamda)^2;
P3=lamda^2/(mu+lamda)^2;
display(P1);
display(P2);
display(P3);
t = 1:5:100 ;
P11 = zeros(size(t)) ; 
P22 = zeros(size(t)) ; 
P33 = zeros(size(t)) ; 
for i = 1:length(t)    
    P11(i)=((mu+lamda)^2)-( 2*lamda)*((mu-lamda)*exp(-(mu-lamda)*t(i))-mu+(lamda*exp(-2*(mu+lamda)*t(i))))-(lamda^2)*(2*exp(-mu*t(i))-2*exp(-(mu+lamda)*t(i))+1-exp(-2*(mu+lamda)*t(i)));
    P22(i)=((-2*lamda)*(mu-lamda)*exp(-(mu+lamda)*t(i))/(lamda+mu)^2)+(2*lamda*mu/(lamda+mu)^2)-2*(lamda)^2*exp(-2*(mu+lamda)*t(i));
    P33(i)=(lamda^2)/(lamda+mu)*((2*exp(-2*mu*t(i)))-(2*exp(-(mu+lamda)*t(i)))-exp(-2*(mu+lamda)*t(i))+1);
end
A=P11;
B=P33;
C=P22;
plot(t,A,t,B,t,C)
legend({'A','B','C'})

Best Answer

Related Solutions

MATLAB: Why exp(a*t) is not equal to ilaplace ((s*i-a)^-1) in matlab

MATLAB: Code for plot figure

Related Question

MATLAB: Why exp(at) is not equal to ilaplace ((si-a)^-1) in matlab