What is the difference between unstable and center subspace? To my knowledge, stable subspace is defined by Eigen vectors where its real part of Eigen values $\mathrm{Re}\,\lambda < 0$.
Unstable subspace is a linear span of those Eigen vectors where $\mathrm{Re}\,\lambda > 0$.
Center subspace - this is where I'm not sure. Is is possible to consider center subspace to be a linear span of those vectors where all $\mathrm{Re}\,\lambda = 0$ or $\mathrm{Re}\,\lambda > 0$ and imaginary part $\mathrm{Im}\,\lambda \neq 0$?
Example:
Let's say I have these 3 Eigen vectors $\left(\lambda_1 = 2,\:\: \lambda_1 = i,\:\: \lambda_3 = -i \right)$:
$\begin{equation} W_1 = (0,0,1) \:\:\:\:\:\:\:\: \textrm{where}\: \textbf{real part:}\:\: U_1 = (0,0,1) \:\:\:\:\:\:\:\: \textrm{and}\: \textbf{imaginary part:}\:\: V_1 = (0,0,0)\,i \\ W_2 = (i,1,0) \\ W_3 = (-i,1,0) \:\:\: \end{equation}$
I understand that unstable subspace is
$E^{U}=\mathrm{span}\{W_1\}$,
because $\mathrm{Re}\,\lambda_1 = 2 > 0$ and $z$ axis $\neq 0$. However, how is it possible that center subspace is
$E^{C}=\mathrm{span}\{U_2,V_2\}$,
and not stable subspace as well - does the imaginary part that is greater than $0$ makes the difference?
Also, how is it possible that $W_3$ doesn't create any subspace at all (at least, I haven't found $W_3$ in the results)?
Thanks