Let $x'(t)=Ax(t)$ be a linear ODE system.
Then the span of the eigenvectors belonging to eigenvalues with negative real-part is called the stable subspace, the subspace spanned by the eigenvectors of eigenvalues of positive real-part is called unstable subspace and the subspace spanned by the eigenvectors belonging to eigenvalues with zero real-part is called centre subspace.
What kind of stability is the stable subspace of?
What kind of unstability (as negation of what kind of stability) is the unstable subspace of?
Is the centre subspace stable or unstable? Are there situation in which it is stable (and which kind of stability then)?