Complex Dynamics

Here's two connections between Linear Algebra and complex dynamics
- given an invertible operator on $\bC^n$,
  it has an induced action on $\CP^{n-1}$,
  who dynamics are often interesting.
  [This is particularly easy for quadratics;
   there the not-semisimple operators are the -parabolic- dynamics,
   while the semisimple ones are (elliptic, hyperbolic, etc.)]

- given a polynomial, take an operator with that characteristic poly
  (this exists by rational normal form)
  If it's invertible, it acts on $\CP^{n-1}$;
  now by fixed point theory it has a fixed point
  (indeed, $n$ of 'em, counted with multiplicity)
  which yields the fundamental theorem of algebra!
  (again, via topology)

Indeed, if you look at the real picture (and $\RP^n$) you also recover
the real versions.

(Also, by looking at the dynamics of a polynomial
 acting on $\CP^1$, you can understand its roots and solving 'em;
 Curt McMullen is very into this)
