Shel asks: << 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 ]

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I think this can be done pretty easily by hand. Any matrix M has to satisfy its characteristic equation P(x) = det(xI - M) = 0, where P is a polynomial of deg = 4. If you write down the first few terms of the series for exp(M), its easy to see how to use P(M) = 0 to express all M^k for k >= 4 in terms of powers of M no greater than the cube. This will yield exp(M) = aI + bM + cM^2 + dM^3, the only problem being that a,b,c,d will be infinite series. (For the skew-symmetric matrix above, though, I expect the series will be familiar ones for simple expressions using well-known analytic functions.) Of course its exp will be a 4D rotation matrix if a,b,c,d are real. Eigenvalues and eigenvectors should be even easier, since each eigenvector of M with eigenvalue lambda is an eigenvector of exp(M) with eigenvalue exp(lambda). Counting multiplicity I think these constitute all eigenvectors of exp(M). --Dan