[PDF] [PDF] PSI* ORAUX 2017 - - - - - - - - - - - - - - - - - - - - - 1 CCP - ENSAM

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????A=0 B BB@a 1a1a1 a a nanan1 C

CCA2 Mn(R)? ??? ??????

?? ???? ??? ?? ???? ?? ?? ???????A? B BB@a 1 a 2??? a n1 C

CCA? ??? ??? ??? ????? ???????A̸= 0? ?????A=0

C C C 1 A ??(A) = 1 ?? ?? ??????=a1+a2++an;A2=0 B BB@a

1 a1a1

a

2 a2a2

a n anan1 C CCA=A ()= 1 ??det(2A??(A)In=

2a12a12a1

2an2an2an

(L1 L1+L2++Ln)

2an2an2an

1 11

2an2an2an

0 B BB@C

1 C1Cn

C

2 C2Cn???

C n1 Cn1Cn1 C CCA=

0 00 1

0 0 2an1

2an n det(2A??(A)In=(1)n+1 00 0 0 n1=2 0 0 n2 det(2A??(A)In= (1)n1n= (1)n1??(A)n ?? ??? ??????? ???? ??u? ????? ??????? ?????? ??g? ?????gou=gog2=g3=g2og=uog? ????x?? ??????? ?????? ??u? ?? ??????i2C??? ???u(x) =ix?i????? ??? ?????? ?????? ??????? ?? ???? ??????Eu(i)??? ?? ?????? ????(x)? g g(x)2Eu(i) =????(x)? ???? ?? ??????2C??? ???g(x) =x? ?? ??? ?????? ??? x??? ?? ??????? ?????? ??g ?? ??????? ??u???? ????? ???? ???∆ =0 B BB@ 100
020 0 0n1 C CCA? B BB@ 100
020 0 0n1 C CCA? g

2=u()D2= ∆() 8i;2i=i

i=1 i ????D=0 B

BB@100

020

0 0 n1

C ?????1= 0????? ??? ????? ?????? ?????? ????C? ? ??????1= 0? ?? ??? ??????i??? ???? ??????? ??????? ????D=0 B

BB@0 00

020

0 0 n1

C < A;B >=??(tA:B)? ?? ????M=0 @0 1 2 2 0 1 11 01 A ??8M2Sn(R);8N2An(R); < W;N >=??(tM:N) =??(M:N) =??(t(M:N)) =??(tN:M) =??(N:M) =??(M:N) =< M;N > ????< M;N >= 0? ?? ??? ?????? ???Sn(R)?An(R)? ???? ?????? ???An(R)(Sn(R))? ?? ?????dim(Sn(R)) =n(n+1) 2 ??dim(An(R)) =n(n1) 2 ?? ????dim(An(R)) =n2dim(Sn(R)) = A n(R) = (Sn(R))? ???? ??????F? 2 {z

2Sn(R)+

MtM 2 {z ??????Sn(R)???p(M) =M+tM 2 ? ????d(M;Sn(R)) =∥Mp(M)∥= MtM 2 ???????M=0 @0 1 2 2 0 1 11 01 A ;Mp(M) =1 2 0 @0 @0 1 2 2 0 1 11 01 A 0 @0 21 1 01

2 1 01

A1 A =1 2 0 @01 3 1 0 2 32 01
A d(M;Sn(R))2= MtM 2 2 =1 4 (0 + 1 + 9 + 1 + 0 + 4 + 9 + 4 + 0) = 7? ???? d(M;Sn(R)) =p 7 H ?=????(In)

M=??(M)

n In| {z

2V ect(In)+M??(M)

n In| {z 2H ????p(M) =M??(M) n In? ???? ?? ??? ???? ?????? ?? ????? ?? ?????? ???q(M) =??(M) n In ??(M) n In 2 =(??(M) n 2 ∥In∥2 {z =1+1+:::+1=n=(??(M))2 n @1 1 1 1 1 1

1 1 11

A 9 3 =p 3

U= maxfX;Yg?V= minfX;Yg?

????U(Ω) =N? 8k2N;(U=k) = [(X=k)\(Y= 1)][[(X=k)\(Y= 2)][ [[(X=k)\(Y=k1)] [[(X=k)\(Y=k)][[(X= 1)\(Y=k)][[(X= 2)\(Y=k)][[[(X=k1)\(Y=k)] k∪ h=1[(X=k)\(Y=h)][k1∪ l=1[(X=l)\(Y=k)]

P(U=k) =k∑

h=1P[(X=k)\(Y=h)] +k1∑ l=1P[(X=l)\(Y=k)] h=1P(X=k)P(Y=h) +k1∑ l=1P(X=l)P(Y=k) =k∑ h=1pq k1pqh1+k1∑ l=1pq l1pqk1 =p2qk1k∑ h=1q h1+p2qk1k1∑ l=1q l1=p2qk11qk

1q+p2qk11qk1

1q =pqk1(1qk+ 1qk1)? ???1q=p?

8k2N; P(U=k) =pqk1(2qkqk1)

8k2N;(V=k) =1∪ h=k[(X=k)\(Y=h)]1∪ l=k+1[(X=l)\(Y=k)]

P(V=k) =1∑

h=kP[(X=k)\(Y=h)] +1∑ l=k+1P[(X=l)\(Y=k)]

P(V=k) =1∑

h=kP(X=k)P(Y=h) +1∑ l=k+1P(X=l)P(Y=k)

1∑

h=kpq k1pqh1+1∑ l=k+1pq l1pqk1 =p2qk11∑ h=kq h1+p2qk11∑ l=k+1q l1=p2qk1(qk1 1q+qk 1q) =pqk1(qk1+qk)

8k2N; P(V=k) =pqk1(qk+qk1)

P[(U;V) = (k;k)] =P(X=k)P(Y=k) =p2q2k2

P[(U;V) = (k;h)] =P(X=k)P(Y=h) +P(X=h)P(Y=k) =p2qk+h2+p2qh+k2= 2p2qh+k2

8(k;h)2N2;P[(U;V) = (k;h)] =8

:0si k < h p

2q2k2si k=h

2p2qh+k2si k > h

8k>2;(U+V=k) = (X+Y=k)

= (X= 1;Y=k1)[(X= 2;Y=k2)[ [(X=k1;Y= 1) k1∪

P(U+V=k) =k1∑

h=1P(X=h)P(Y=kh) =k1∑ h=1pq h1pqkh1=p2k1∑ h=1q k2

8k>2;P(U+V=k) =p2(k1)qk2

??E(U+V) =1∑ k=2kP(U+V=k) =p21∑ k=2k(k1)qk2 ?? ???? ??? ?8x2]1;1[;1∑ k=0x k=1 k=0kx k1=1 (1x)2??1∑ k=0k(k1)xk2=2 (1x)3 ???? ?E(U+V) =p21∑ k=2k(k1)qk2=2p2 (1q)3=2 p

E(U+V) =2

p ???A=0 @1 11 1 33 2 221 A

?? ??????? ???E= ker(f2)ker(f2IdE)??? ?????? ?? ??????? ??ker(f2)ker(f)??? ??????? ????? ?????? ??? ????B′??E????? ???MatB′(f) =0

@0 1 0 0 0 0

0 0 21

A ?? ????g2L(E)??? ???g2=f? ??????? ???ker(f2)??? ?????? ???g? ??? ??????? ?? ??????? ? ker(f2)\ker(f2IdE) =f0g? A 2=0 @2 22 2 22

0 0 01

A dim(kerf2) = 31 = 2?

A2I3=0

@1 11 1 13 2 241 A {ker(f2)ker(f2IdE)E dim(ker(f2)ker(f2IdE)) = dim(ker(f2)) + dim(ker(f2IdE)) = 2 + 1 = 3 = dim(E) ker(f2)ker(f2IdE) =E ?? ????x2E? ?? ??????? ???????X=0 @1 0quotesdbs_dbs16.pdfusesText_22

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