(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that A is a 6x6 matrix with real values and has a min. poly of p(s) = s^3.

a) Find the Characteristic polynomial of A

b) What are the possibilities for the Jordan form of A?

c) What are the possibilities of the rank of A?

2. Relevant equations

See below.

3. The attempt at a solution

a) I only see that 3 of the eigenvalues are zero, but dont know how to find the rest for the characterisitic polynomial

b) The Jordan blocks can be size 1,2, or 3 i.e. [L 1 0; 0 L 1; 0 0 L], [L 0 0; 0 L 0; 0 0 L], [L 1 0; 0 L 0; 0 0 L] where L are the eigenvalues from the min. poly. (equal to zero)

c) rank(A) + dim N(A) = n, where N(A) is the nullspace of A, and n = 6. Do I just need to find the nullspace of A (and if so, how?) or am I going down the wrong direction.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Minimal Polynomial and Jordan Form

**Physics Forums | Science Articles, Homework Help, Discussion**