Hi all i need a little help with Jordan form

[panoskarti]

ok this is my problem...
i have diagonalized the A matrix with the equation P^-1*A*P
and the result is J=[-1 0 0;0 2 1; 0 0 2]. in order to find the e^Jt do i need to do the following? =>


[-e^t t*e^t 1/2*t^2 *e^t

0 2*e^t t*e^t

0 0 2*e^t]


I am not sure about the 2 and 3 elements in the first row of the matrix since i have zeros at the J matrix but a mathematics book confused me..

Thanks in advance..

 

[panoskarti]

i did a mistake this is the matrix..

[e^-t t*e^t 1/2*t^2 *e^t

0 e^2t t*e^t

0 0 e^2t ]

 

[tacman]

Hi there,

It looks like you are on the right track! In order to find e^Jt, you do need to use the formula e^Jt = Pe^(Jt)P^-1, where J is your Jordan form matrix and P is the matrix that diagonalizes A.

In your case, since J has zeros in the second and third elements of the first row, those elements will also be zero in your final result. So your calculation should look something like this:

[-e^t 0 0;
0 2*e^t t*e^t;
0 0 2*e^t]

I'm not sure what the book said that confused you, but hopefully this helps clarify things. Good luck with your problem!