17/3/20 he

f E Errol W )

A E Mn ( K ) .

P E K EX ]

p CX) = a.

ta,X t - - -

t adXd

p (f) = do It a,

f t.

. .

t adf'd

p (A)= do Int a,

At . . toeaAd feud

C-Mn (K)

Se A = MB (f) ⇒

p CA) = MB ( p Cf ) ) .Perche :

perche MB ( ft g) = MBA)tMB(g)

Nofx f) ⇒ MBA)

MBA' ' ) -

- MBA)"

.

EES. Se A. B mctwciorme .

B -- CAC

- '

CE Gluck )

⇒ PCB ) -- CPCAK

- '.

(perche CCAC- 'JE CA -4¥!

. .

= CAKE ! )

OIS . important .

f- E End (V ),

Ae Mulk )

p , 9 E K ⇒

PA ) e qcf ) (PCA) eggs) )

COMMUNARD ..

pfftqff ) = qff ) Pff )

p NAK q (A) PCA) .

p = a. t ai Xt. . .

t adXd

q = bot b. Xt . - -

t b,

X'

pff ) q (f) = (ao It aft . - . tadfd) .

( b Etb,

ft. . . tbgfd )

do I be I t AOI b,

ft a ,f b. I t

Ian. II.s 't'

as'tb.if'tIII. It. . )

Rob .I t Rob

, Iff t a , bo IIf-

+ ( Rob,

I f2

t Q ,b

,f- f tdzbof ? It

..

qfft.PH/= . . .

he Deme cos a

fkfe = fl .fk =

fktl.

papalf- REX ] → End (V )

Alkfxt.to#MnfikfMB

Quester appt . some om.

di

ourelli

some ouche in patrol . linear

come apple .True K - op . vetl

.

dim, k

IK CX ] = N

dim,k

End (V ) ooh 'm,k

Mnflk)e- fine ,

il make e- to

Il mucho E nu r oleateMONICO

G- et en. ore unpalimonyoff ( X ) t

. a . 9pct ) = 0

Be p I un polimowo

T.c.pe/--o ⇒ p e-

divisible per off .

(off E ie pal .moves di

grade minims che camille

f- )Def . ff si dice ie palinode

MINI MO di f.

Es . ( 33) = A

morrone ele 9A XI 3×+2 -

( che e- aude ie pal .

conatlevstrco ) .

teared( variant old CRT )

Sia p E IK Ex ] t . c .

PG ) =D.

Se p =p ,

. pz .

⇒P , Pz PRI MI TRA LORO

V = Ker p , A) a Ker Pdf )DIS.

Kev P, (f) e Ker Bff ) sore

SSU f - INVARIANT

EI .Se f E End ( v ) T

. a .

f-2

- 5ft GI =D

-

(V op . vetloviele 10h )

⇒ f e- diagonalize .

per ie terrene

p = X 2-5×+6 =(X- 2) (x - 3)P , Pz

V = Ker ( f - ZI ) Korff -3 I )-

-

Vz V3.

Coralloid f E End

PE IKCXT Pff )=0

p = Ps .

- --

' Pa

Ps , - - - pre a due a due'

prime true lone.

⇒ V -

- IOI,

Ker Pi Cf )

For f - in.

Dim .old corollaries per ind

m k.

Pa e Pi . . ..

' Pre primitivelove

V = Ker p ,Cf) 0 Ker ( Pi . . .

.

pre Cf))-

f - innovate

Pz ; - - . pre

a due a ohne

prow to here

i pretend indnthrs a

f-I

Ker ( pi . - -

' Puff ) )Ker ( pi . . .

. paced) = ¥7 kerpiff ) .

Dim del Teorenna :

pooches Ps e pz some

prime true hero,

esrsrere

a,

b Elk t. c .

I = a pztbpz .

Caladium guerre iol.

oh '

polo men on f

I = a Pff ) t b (f) Pdf )W#wmreno

V c- V.

rneeae

v -- a ftp.ffkvltbfftpzffkv )

v -- a ftp.ffkvltbfftpzffkv )

-

pitsaw pet

'tfPaff) (t

) = O

" "ex . . .

c- kerpzff)

⇒

V

= kerpzffltkerp ,

per mostnere ie tear

debts some master che

Ker RCH n Ker Paff ) -401

Er-

v -- a ftp.fftfhtbfftpzffkv ) ⇐00

- -

a O a 0

DEI si he anele

Kerk CH = Im Pdf )

Ker Pdf ) = Imp , CH .

Is .V sp . well . sulk f. d

.

alg .chime

.

off ie one pet . mimmo.

9fG ) = II ( X - a)mi

Li - - - du coolieDISMNTE

se it j ( X - di )me( X - g) mi

see

µCRT pin 'Re

here

V = Korff - L,

- E)MY

Teared ( Cayley - Hamilton )

f euohemorfismo

( A matric quadrate )

Sie Pf ie no pdimowo

cometteristico pffx) = oletff -

XI )⇒ pelf ) = 0

-

Coralloid ie pal . minim

off divide ie pot .comet

. Pf .

D imootniemo C - H we case

f- or a Triangdabte .

( Chiaramonte se A = MBA)e PA e- ie no pal .

could.

ba@amootronepACAJ-Ote1a9ioii.9.jBe A -

- (a "

o

'

'

.

amPaff'M= @u - X ) Cau - X) :

. . .

.

Pf (f) = Cant - f) faut - f ) . . . .

- -

§, -. . Vn } = B

!

fCv,)=aTf- ( Vz ) = Azz Vz t Rizvi

;

f- Cvn ) = Amrut - - -

Pf (f) CVD = @uI - f ) .

. - ( aunt -FIND= ( azzi - f )

. . . @nnI - f) Can I - f) (VD

=D-

pfff) Cvd = ( - - faut⑦ Cheat- f )) (Vz)

ee cosi via

Pfff) Vi = o fit . - . n

⇒ peg )=o ! !- .

- . -