# Jordan Normal Forms

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• Dec 10th 2013, 05:59 AM
Matt1993
Jordan Normal Forms
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: P2 --> P2 given by T(p(x)) = p(x+1)

Thankss any help is appreciated. I not great at JNF
• Dec 10th 2013, 09:22 PM
chiro
Re: Jordan Normal Forms
Hey Matt1993.

Just out of curiosity, what is the space P2?
• Dec 10th 2013, 09:32 PM
romsek
Re: Jordan Normal Forms
I'm gonna guess that's the space of 2nd order polynomials
• Dec 10th 2013, 10:00 PM
romsek
Re: Jordan Normal Forms
Quote:

Originally Posted by Matt1993
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: P2 --> P2 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 x2

p(x+1) = (a0+a1+a2) + (a1 + 2 a2) x + a2 x2

In other words

$\displaystyle T(p) =\left(\begin{array}{ccc}1 & 1 & 1\\0 & 1 & 2\\0 & 0 & 1\end{array}\right)$

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.