2 Find the characteristic polynomial and the minimal the cha

2 Find the characteristic polynomial and the minimal the characteristic polynomial and the minimal polynomial o th operator N in Example 8.54. Cnnnnea A, M 1,1 :.. . Dra va that the minimal polvnomi\" Deruia that the minimal polvnomini

Solution

Here the matrix (say A) of N with respect to the basis {N²v₁, Nv₁, v₁, Nv₂, v₂, v₃} as obtained, gives the Characteristic polynomial det(A-xI)= 0 , i.e. x⁶= 0.

Clearly A is represented in the Jordan Canonical form having 3 Jordan 0-blocks of size 3, 2 and 1. So the Minimal polynomial is x³=0.