Jordan canonical form
General · Mathematics
Study notes
Q: Find the Jordan form of [[2,1],[0,2]]. Is it diagonalizable? Eigenvalue: 2 (double). Eigenspace: [[0,1],[0,0]]v = 0: span{(1,0)}: dim 1. Geometric mult 1 < 2: DEFECTIVE! Jordan form: single block J₂(2) = [[2,1],[0,2]] (already!). Not diagonalizable! (One block: one eigenvector!)