Find the Rational Canonical form of the linear transformation over the space $ \ \mathbb{Q} \ $ whose elementary divisors are $ \ (x^2+x+1)^2 , \ (x^2+x+1) \ \ and \ \ (x^2+2)^2 \ $.
Answer:
Since the divisors are $ \ \ (x^2+x+1)^2 , \ (x^2+x+1) \ \ and \ \ (x^2+2)^2 \ $ , the minimal polynomial $ \ m(x) \ $ is given by
$ m(x)=(x^2+x+1)^2 (x^2+x+1) (x^2+2)^2 =(x^2+x+1)^3 (x^2+2)^2 $
But I am unable to find the Rational Canonical Form (RCF) .