Question

How to bring to the canonical form Jordan matrix:`A=[(-1,1,1),(-3,2,2),(-1,1,1)]`?

Answer 1

See below.

Explanation:

Taking the matrix `A` characteristic polynomial and then finding it's roots

`det(A-lambda I) = -lambda(lambda-1)^2` and then with `lambda_1= 0,lambda_2=lambda_3=1` we form

`J = ((lambda_1, 0, 0),(0, lambda_2, 1),(0, 0, lambda_2))` or

`J = ((0, 0, 0),(0, 1, 1),(0, 0, 1))`

Note the submatrix due to `lambda_2=lambda_3`

`s_2 = ((lambda_2,1),(0,lambda_2))`