B Linear Differential Equations
139
The extension to complex-valued λ and/or initial condition q 0 is simple since the
resulting complex-valued solution q(t) is defined on the real line so that it can be
viewed as a two-dimensional vector whose components are its real and imaginary
parts. Alternatively, we note that the above operations are also valid for complexvalued functions defined on the real line such as q(t) so that q(t) in Eq. B.12 solves
Eq. B.11 for complex-valued λ and/or initial condition q 0 .
139
The extension to complex-valued λ and/or initial condition q 0 is simple since the
resulting complex-valued solution q(t) is defined on the real line so that it can be
viewed as a two-dimensional vector whose components are its real and imaginary
parts. Alternatively, we note that the above operations are also valid for complexvalued functions defined on the real line such as q(t) so that q(t) in Eq. B.12 solves
Eq. B.11 for complex-valued λ and/or initial condition q 0 .