> Can I generate the series approximation (in symbolic variables) in Maxima, for the exponential/matrix exponential?
Try
(%i6) m : matrix([0,x],[-x,0])$
(%i7) larry(mat,n) := sum(mat^^k / k!,k,0,n-1)$
(%i8) larry(m, 5);
(%o8) matrix([x^4/24-x^2/2+1,x-x^3/6],[x^3/6-x,x^4/24-x^2/2+1])
A Horner method for summing I + mat + mat^2 / 2 + ... might boost the speed.
--Barton