Question

please answer #6 a and b, my 6d from previous assignment is shown in 2nd picture

6. a. Show that if N E C(H) is nilpotent then ơr(N) 0, (use 6d fron last assignment). b. List the similarity classes of the (nonzero) nipotent linear maps of a 5- dimensional vector space overE i.e., give a representative matrix in each class) d) N is nilpotent z-3n such that Nn , D T-Nisinvertible wit'h inverse ANAN .

Answer 1

q)Given +he lineaづ +-s@ngpos malom NEL es nid poterd We have fos every }íneastaa/nstoブ Ho r, say uch tha So n ni) pot end if and only cf月 is nilpotond Then setspies shepor So an ennhi laking pelt

o g dha agen ce v hous oimension chauactesestic ayp eoch to each }i neda bo minima polgromials can *hen When minimal polmomia The Jorolan matsio OOOo ocoo

꼭"Nhon menirnaj polarnornal, cs Tha Josdlan matsi cam 2 when tha minima po

The Joadan matscescam b

ol /4 占 OOOC 7 o O OO o

F01 each matai, ni e go a lineaづto Posmatiorm 50 we pet nilpotend linoan maps of a 5-okimom6i ơnaj ane