Hey Matt1993.
Just out of curiosity, what is the space P2?
I am trying to revise for a test and i cannot get this question. And i have know idea where to start.
Question
Find the JNF for the matrix of the linear transformation T: P_{2} --> P_{2} given by T(p(x)) = p(x+1)
Thankss any help is appreciated. I not great at JNF
eh I think the easiest way to go about this is just brute force it.
let p(x) = a0 + a1 x + a2 x^{2}
p(x+1) = (a0+a1+a2) + (a1 + 2 a2) x + a2 x^{2}
In other words
you can mull on that if it helps while I read up on JCF.
The next step is to find the eigenvalues and vectors for this matrix.