Hi all i need a little help with Jordan form

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SUMMARY

The discussion centers on the computation of the matrix exponential e^Jt for a diagonalized matrix J, specifically J = diag(-1, 2, 2) represented as J = [[-1, 0, 0], [0, 2, 1], [0, 0, 2]]. The correct form of e^Jt is confirmed to be [[e^-t, t*e^t, (1/2)*t^2*e^t], [0, e^(2t), t*e^t], [0, 0, e^(2t)]]. The user expresses uncertainty regarding the off-diagonal elements in the first row, which are clarified through the correct application of matrix exponential rules.

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panoskarti
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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..
 
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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 ]
 

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