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

of

. From here it follows at once that N is nilpotent, and check that

but

, so that its Jordan Form is...

Tonio