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Example of Jordan Canonical Form: Real 4x4 Matrix with Basis 1

Matrix Theory: Find a matrix P that puts the real 4x4 matrix A = [2 0 0 0 \ 0 2 1 0 \ 0 0 2 0 \ 1 0 0 2 ] in Jordan Canonical Form. We show how to find a basis that gives P. The Jordan form has 2 Jordan blocks of size 2.
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