- #1
gottfried
- 119
- 0
I've been given a matrix A and calculated the characteristic polynomial. Which is (1-λ)5. Given this how does one calculate the minimal polynomial?
Also just to check, is it correct that the minimal polynomial is the monic polynomial with lowest degree that satisfies M(A)=0 and that all the irreducible factors of the minimal polynomial divide the characteristic polynomial?
Given this I think the minimal polynomial is (1-λ)2 since (I-A)≠0 and (I-A)2=0 but this method to figure it out seems a little ad hoc.
A=
[1 1 0 0 0]
[0 1 0 0 0]
[0 0 1 1 0]
[0 0 0 1 0]
[0 0 0 0 1]
Also just to check, is it correct that the minimal polynomial is the monic polynomial with lowest degree that satisfies M(A)=0 and that all the irreducible factors of the minimal polynomial divide the characteristic polynomial?
Given this I think the minimal polynomial is (1-λ)2 since (I-A)≠0 and (I-A)2=0 but this method to figure it out seems a little ad hoc.
A=
[1 1 0 0 0]
[0 1 0 0 0]
[0 0 1 1 0]
[0 0 0 1 0]
[0 0 0 0 1]