If T: V→V is a linear transformation, and V is a vector space. Does there exist a sequence of subspaces {0} =U_0⊆U_1⊆U_2 ⊆···⊆U_n =V such that Dim(U_i) =I for all I and T [U_i] =U_i for I=1,2,…,(n-1)?
valid question