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Jordan Canonical form of a matrix

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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.

I am not clear what to do with the complex eigenvalues, and I am not sure how to view the entire matrix. By that I mean, I am not confident that examining the matrix as a smaller (2x2) block is heading me in the right direction.

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Solution Summary

The process of fundung Jordan Canonoical form of a matrix is explained and illustrated with an example of a 4x4 matrix.
The solution is in PDF format.

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