Jordan form help...

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December 6th 2009, 12:55 PM
Majialin

Jordan form help...

I stumbled across this question, and I'm not quite sure how to go about and find the Jordan form of this kind of question. Any help on how to get started?

Let
N be an element of L(P4(C)), defined by N(p(z)) = zp'''(z)+p'(z).Show that N is nilpotent and find the Jordan form of N.

Any help is greatly appreciated!
December 7th 2009, 07:32 AM
GreenDay14

I am also curious as to the solution of this problem
December 7th 2009, 12:35 PM
tonio

Quote:

Originally Posted by Majialin

I stumbled across this question, and I'm not quite sure how to go about and find the Jordan form of this kind of question. Any help on how to get started?

Let

N be an element of L(P4(C)), defined by N(p(z)) = zp'''(z)+p'(z).Show that N is nilpotent and find the Jordan form of N.

Any help is greatly appreciated!

Find the matricial representation of N wrt the basis $\{1,z,z^2,z^3,z^4\}$ of $P_4(\mathbb{C})[z]$ . From here it follows at once that N is nilpotent, and check that $N^5=0$ but $N^4\ne 0$ , so that its Jordan Form is...

Tonio