Critical Points of Linear Autonomous Systems

eigenvalues			linear system
real	both pos.	equal	proper or improper^* node	unstable
	both pos.	different	node	unstable
	both neg.	equal	proper or improper^* node	as. stable
	both neg.	different	node	as. stable
	pos. and neg.		saddle point	unstable
complex not real	real part pos.		spiral point	unstable
	real part neg.		spiral point	as. stable
	real part zero		center	stable

^*Note: For two equal real eigenvalues we obtain a proper node if there are two eigenvectors. If there is only one eigenvector we obtain an improper node.