General solution to y = exp(c_i T_i)x?

uekstrom

I hope this is the right subforum. Anyway,

is there a general solution to

[tex]y = \exp\left(\sum_i c_i T_i\right)x[/tex]

for given real vectors x,y (|x|=|y|) and anti-symmetric matrices [tex]T_i[/tex]?

For the one dimensional case I managed to show that [tex]y^{\dag}\exp(cT)x[/tex] is extremized for c = pi/2 + atan( -y'T^2x / y'Tx ) + n pi, if T is normalized such that it has eigenvalues -i,0,i.

Is there a similar formula for the general case?