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  +        ###Learning more
  +        We've really only scratched the surface of what linear algebra is all about. To learn more, check out the legendary Gilbert Strang's [Linear Algebra](http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/least-squares-determinants-and-eigenvalues/eigenvalues-and-eigenvectors/) course at MIT's Open Courseware site. To get more practice with applications of eigenvalues/vectors, also ceck out the excellent [Differential Equations](http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/) site.
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          Here, $1+i$ is an eigenvalue and $(1, i)$ is an eigenvector. 
  
          Whenever a matrix has complex eigenvalues, the system it describes will spiral around $(0,0)$. To see this, drag $A$'s columns (the arrows) around until you get a spiral. The eigenvalues are plotted in the real/imaginary plane to the right. You'll see that whenever the eigenvalues have an imaginary part, the system spirals, no matter where you start things off.
  
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            As you can see, the system goes toward the grey line, which is an eigenspace with  $\lambda = (1+\sqrt 5)/2 > 1$.
  
            ###Steady States
  
            Suppose that, every year, a fraction $p$ of New Yorkers move to California and a fraction $q$ of Californians move to New York. Drag the circles to decide these fractions and the number starting in each state.
  
  