I have a question about jordan form and basis but i'm having a really hard time understanding it if any one could look and at least lead me in the right direction. Thanks!
Suppose that T ∈ L(C5) and its matrix in standard basis is as following.
5 1 0 0 0
0 5 0 0 2
0 0 2 0 3
0 0 0 2 4
0 0 0 0 5
Find the Jordan form, the Jordan basis, and also the minimal polynomial of T
I found 5,5,5,2,2 as eigenvalues and know they go along the diagonal but i'm not sure how to find out about the ones that go ontop of those numbers? Thanks


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