My textbook on dynamical systems says that a dynamical system written as:
$\mathbf{x'} = \mathbf{f(x)}$,
where the right-hand-side $\mathbf{f(x)}$ is a vector field defined on a manifold equivalent to the dimension of the system. My question is that if this is a linear system, where $\mathbf{f(x)} = A\mathbf{x}$, is this still defined on a manifold?
Thanks.
Thomas