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

I hope this is the right subforum. Anyway,

is there a general solution to

$$y = \exp\left(\sum_i c_i T_i\right)x$$

for given real vectors x,y (|x|=|y|) and anti-symmetric matrices $$T_i$$?

For the one dimensional case I managed to show that $$y^{\dag}\exp(cT)x$$ 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?
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