Question: Find a basis for each generalized eigenvalue of consisting of a union of disjoint cycles of generalized eigenvalues. Then find a Jordon canonical form of . The matrix given is:
[11 -4 -5
21 -8 -11
3 -1 0]
My attempt: So the characteristic matrix is , which gives with multiplicities of respectively. Then and . Specifically, and . I managed to find a basis for , which is
[1
3
0]
But when I tried it for , I got:
[9 -4 -5
21 -10 -11
3 -1 -2]^2 x = 0
which provides a basis with dimension 3, which makes no sense. Any hints, please? Thanks!