- #1
Locoism
- 81
- 0
Homework Statement
Given the invariant factors of the matrix λI - A are
d1 to d5 = 1, d6 = (λ-3)(λ-2)2 , d7 = (λ-3)2(λ-2)2
Display the rational canonical form of A
Display the Jordan canonical form of A
The Attempt at a Solution
I'm half guessing here, but we have for d6 : λ3 - 7λ2 + 16λ - 12
and for d7 : λ4 - 10λ3 + 13λ2 + 12λ + 36
Would the rational canonical form be a diagonal block matrix (sorry for the formatting)
A | 0
0 | B
with A =
0 0 12
1 0 -16
0 1 7
and B =
0 0 0 -36
1 0 0 -12
0 1 0 -13
0 0 1 10
or would it be a 7x7 block matrix with the first 5 diagonals = [1]?
For the Jordan form I just need to find the eigenvectors and put them in the same block matrix form, right?