Difference between improper node and proper node for phase portrait Can someone offer an explanation for the difference between these two?  I see pictures of what seem to be examples of both, but it's hard for me to discern what a new portrait would be.
Any help?
Thank you!
 A: To amplify @Artem's answer: 
When there are two distinct real eigenvalues, there are two real eigenvectors, and each trajectory in the phase portrait must be nearly parallel to one of the eigenvectors when the trajectory is near the fixed point, and nearly parallel to the other eigenvector when the trajectory is far from the fixed point. 
When there is a repeated eigenvalue, and only one real eigenvector, the trajectories must be nearly parallel to the eigenvector, both when near and when far from the fixed point. To do this, they must "turn around". E.g., if the eigenvector is (any nonzero multiple of) $(1,0)$, a trajectory may leave the origin heading nearly horizontally to the right, then farther away from the origin start curving around to the left, until it has "done a 180" and is heading nearly horizontally to the left. 
A: The proper node is that you have two eigenvalues of the same sign. In the basis of the eigenvectors the phase orbits look like "parabolas". The improper node corresponds to the case when you have one eigenvalue multiplicity two. It is very similar to the proper node in many respects, however, the orbits are not "parabolas". It is possible to say that improper node looks like something between a node and a focus. 
