Using eigenvectors to determine nature of saddle point
I've determined that in an autonomous system, there is a critical point at the point (2, -0.4), then looking back at the system determined the eigenvalues associated with this point tell us that the point is a saddle point. From this, the eigenvectors are (1, -2/3) and (1, 0.4), but I don't understand what the eigenvectors are telling us about the "rotation" of the saddle point.
Can anyone shed some light on this for me?
Re: Using eigenvectors to determine nature of saddle point
Draw lines through the point in the direction of those eigenvectors. Since you say the eigenvalues tell us that the point is a saddle point, there must be one positive and one negative eigenvalue. Draw an "arrow" pointing away from the point on the line corresponding to the positive eigenvalue and an "arrow" pointing toward the point on the line corresponding to the negative eigenvalue. The "flow" lines around the point will lie within those lines and their direction will be the same as on the lines near them.