Given $T : \mathbb{R}^3 \to \mathbb{R}^3$ such that $T(v) = A v$ where $A = \begin{matrix} 2 && 0 && 0\\1&& 2 && 0 \\ 0 && 0 && 3 \end{matrix} $
I want to find all T-invariant :
I know that $\mathbb{R}^3 , \{0\}$ are such sub-spaces,
Also $f_T(x) = (x-2)^2 (x-3)$ so all other T-invariant sub-spaces are :
$Ker(A-2 I) , Ker(A-3I) , Ker((A-2I)^2) , Ker((A-2I)(A-3I))$
Is this correct, or is there something wrong ?