Example 4

The differential operator on the space of polynomials of degree less than or equal to three is represented in the "natural" ordered basis by the matrix D. Compare the size of the Jordan block for each eigenvalue with the multiplicity of that eigenvalue in the minimal polynomial for the matrix D, using the techniques learned above. YOU try it.

In[55]:=

  d={{0,1,0,0},{0,0,2,0},{0,0,0,3},{0,0,0,0}};
  MatrixForm[d]

Out[55]=

  0   1   0   0
  
  0   0   2   0
  
  0   0   0   3
  
  0   0   0   0

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