Recent content by anastasis

i see that p(A)=0 and that p(A)=A^n +...+det(A) BUT I'm still a bit confused by some details. A is nilpotent <=> A^k=0 ... must show k=n for one thing.

How do I show that the cp of A is p(x)=x^n, dimA=n?

Homework Statement How do I show that the cp is p(x)=x^n, dimA=n? Homework Equations A^k=0 for some k (obviously need to show k=n); p(A)=0 The Attempt at a Solution p(A)=0 <=> A^n + ... + det(A)=0