Evaluate eAt
Where A is an upper triangular matrix given by
1 2 3
0 1 2
0 0 1
What is the answer? Determinent is obviously 1...
I just had that question on my diff eqns test I had no idea how to do it. I'm not sure if he talked about it in class since I don't go. :-[
I took linear algebra about a year ago so I've forgotten a lot of stuff.
http://mathworld.wolfram.com/MatrixExponential.html
Quote from: Yoni on July 20, 2006, 03:48 PM
http://mathworld.wolfram.com/MatrixExponential.html
ok... I think this is how you do it.
A is equal to
[ 0 2 3 ] [ 1 0 0 ]
[ 0 0 2 ] + [ 0 1 0 ]
[ 0 0 0 ] [ 0 0 1 ]
Let B be the matrix on the left.
Then exp(At) is equal to exp(t(B+I)) where I is the identity matrix.
This then gives us exp(tB)exp(tI)
B is a nilpotent matrix, but I don't know how to get the matrix polynomial. I think someone said it has to do with taylor polynomials.
Oh well...
Your evaluation is not correct. exp(A+B) != exp(A) + exp(B).
Quote from: Yoni on July 21, 2006, 04:01 AM
Your evaluation is not correct. exp(A+B) != exp(A) + exp(B).
err, stupid mistake. :-[
fixed.
Argh, I studied this for the final and he didn't put it on there.