An Example of Expression Swell

• consider the Hankel matrix

  
  
  

• it has the following characteristic polynomial:

  
  
  

• the Hankel matrix has four zero eigenvalues, one eigenvalue is -6, and the other four eigenvalues are roots of the seemingly simple looking quartic polynomial

  
  
  

• here is one root of this quartic polynomial

  
  
  
  
  

• the other three roots are similar in structure.