Consider, more generally, [ 0 a -b c] [-a 0 d e] = M. [ b -d 0 f] [-c -e -f 0] Maple calculates the characteristic polynomial to be x^4 + (aa+bb+cc+dd+ee+ff) x^2 + (af+cd+be)^2 = 0. The eigenvalues are +iA, -iA, +iB, -iB, with A and B messy real-valued expressions (assuming a, ..., f are real). R = exp(M) is a 4-dimensional rotation. There is a pair of orthogonal planes P1 and P2 (determined by the eigenvectors of M) such that R is the commutative product of a rotation by angle A in P1 with P2 fixed, and a rotation by angle B in P2 with P1 fixed. --- Shel Kaphan <sjk@kaphan.org> wrote:
Is anyone's symbolic math package able to take the matrix exponential of
[ 0 a 0 -d ] [ -a 0 b 0 ] [ 0 -b 0 c ] [ d 0 -c 0 ]
?
I set Macsyma to work on it, and it seems only to be trying to melt my laptop and burn the house down after long enough to suspect it isn't going to finish.
If a result of that is available, I'd also like to know the resulting eigenvalues and eigenvectors.
Thanks in advance,
Shel
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