anchor.diff:            fibonacci-sequence
   
           :markdown
  -          As you can see, the system goes toward the grey line, which is an eigenspace of the matrix.
  -
  -          ###Markov Chains
  +          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.
   
  
positive.code:       :markdown
          #Complex eigenvalues
  
          So far we've only looked at systems with __real__ eigenvalues. But looking at the equation  $ Av = \lambda v$, who's to say $\lambda$ and $v$ can't have some imaginary part? For example, you can verify that
  
        script(type="math/tex; mode=display").
            \begin{pmatrix}
  
negative.code: 
          :markdown
  
          p
            :markdown
              If you can draw a line through $(0,0)$, $v$ and $Av$, then $Av$ is just $v$ multiplied by number $\lambda$; that is, $Av = \lambda v$. In this case, we call $\lambda$ an __eigenvalue__ and $v$ an __eigenvector__. For example, here $(1,2)$ is an eigvector and $5$ an eigenvalue.
  