Question:
Jordan Canonical form of a matrix
For the given 4x4 matrix, find P such that INV(P)AP is in Jordan Canonical Form.
A = | 2 1 0 0 |
| -1 4 0 0 |
| 0 0 2 1 |
| 0 0 -1 2 |
It is easy to find repeated eigenvalues (3, 2+i, 2-i).
If I treat the upper block as a 2x2 matrix, I can find P = [1 0; 1 1] (Note: Using Matlab notation here). This correctly results in INV(P)AP = [3 1; 0 3] which is in the form needed.