Jordan Forms, Nullity and Minimal Polynomials

[shaon0]

Homework Statement

Nullity(B-5I)=2 and Nullity(B-5I)^2=5
Characteristic poly is: (λ-5)^12
Find the possible jordan forms of B and the minimal polynomials for each of these JFs.

The Attempt at a Solution

JFs: J_n1(5) or ... or J_ni(5).
Not sure how to find these jordan forms and minimal polynomials.

 

[shaon0]

Homework Statement

Nullity(B-5I)=2 and Nullity(B-5I)^2=5
Characteristic poly is: (λ-5)^12
Find the possible jordan forms of B and the minimal polynomials for each of these JFs.

The Attempt at a Solution

JFs: J_n1(5) or ... or J_ni(5).
Not sure how to find these jordan forms and minimal polynomials.

Bump

 

[HallsofIvy]

What does "minimal polynomial" for a matrix mean? What do you know about the relation between the minimal polynomial of a matrix and its eigenvectors?