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.
- Real, distinct, both negative.
- Real, distinct, both positive.
- Real, distinct, of opposite
signs.
- Repeated and negative, with
one-dimensional eigenspace.
- Repeated and positive, with
one-dimensional eigenspace.
- One zero, one nonzero.
- Complex with negative real part.
- Complex with positive real part.
- Pure imaginary.
