Trajectories of Linear Systems

Part 4: Summary

Describe in words the phase portrait of the 2x2 system of differential equations X' = A X for each of the following descriptions of eigenvalues of A.

1. Real, distinct, both negative.
2. Real, distinct, both positive.
3. Real, distinct, of opposite signs.
4. Repeated and negative, with one-dimensional eigenspace.
5. Repeated and positive, with one-dimensional eigenspace.
6. One zero, one nonzero.
7. Complex with negative real part.
8. Complex with positive real part.
9. Pure imaginary.