Exercises

1. Find the Jordan form J and the matrix S such that Inv(S)BS=J for
B={{2,1,1}, {0,2,1},{0,0,-1}}. Do not forget to clear matrices that were previously used. Check using the JordanDecomposition command.

2. Find the Jordan form J and the matrix S such that Inv(S)BS=J for
B={{0,1,2}, {0,0,1},{0,0,0}}. Do not forget to clear matrices that were previously used. Check using the JordanDecomposition command.

3. If A is a complex 5 by 5 matrix with characteristic polynomial (x-2)^3(x+7)^2 and minimal polynomial (x-2)^2(x+7), what is the Jordan form of A? Mathematica not needed!

4. How many possible Jordan forms are there for a 6 by 6 complex matrix with characteristic polynomial (x+2)^4(x-1)^2?
Mathematica not needed.

5. Find the Jordan form J and the matrix S such that Inv(S)BS=J for
B = {{6, -3, 0, 9}, {0, 3, 0, 0}, {2, 1, 3, 2}, {-3, 2, 0, -6}}. Do not forget to clear matrices that were previously used. Check using the JordanDecomposition command.

Up to Jordan Canonical Form