I'm trying to find all the possibles Jordan normal form of a linear map called $T$: $\mathbb{Q}^3$ → $\mathbb{Q}^3$ such that $(T^7+2I)(T^2+3T+2I)^2=0$.
So I am a little confuse because I know that to find the Jordan normal form I need the eigenvalues and the eigenvector of the linear transformation. But how can i find the matrix associated with T?