????????????:?????????,?????? n ????,?????????????? k ??????,????? m ???????????? - PowerPoint PPT Presentation

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????????????:?????????,?????? n ????,?????????????? k ??????,????? m ????????????

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Title: 1 Author: Song Peng Last modified by: Created Date: 12/10/2002 6:43:43 AM Document presentation format: – PowerPoint PPT presentation

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Title: ????????????:?????????,?????? n ????,?????????????? k ??????,????? m ????????????

1
??? ???

7.1 ????????
7.2 ??????
7.3 ????????
7.4 ??????
7.5 ??????????????
7.6 ??????????
7.7 ????????
7.8 ????????
7.9 ????????

2
7.1 ????????

???(?????)??????????1955????
?????????????????????,?????? n
????,?????????????? k ??????,????? m ????????????
???????? R ?,???????????,?????????
????????
??????????????????
????
??????????????
???????????????

3
7.1 ????????

(1) ?????????????????
?7.1 (2,1,3)?
???????????9.1
?????????? M
?????? M ??????,???? k ???????,???????,k
???????????
???? (m1) ?????????,?????????? k ????
g(i,j)???????,i1,2,,kj1,2,,n?? nk ?????
g(i,j) 1?,??????????????? g(i,j)
0?,????????????? k(m1) ?????,??????? nk(m1)
???????
?? K ???????? n ?,?????? k ??????? n ????

4
7.1 ????????
5
7.1 ????????

???? Mm0(1)m1(1)
ml(1)??? l ????? k1????
????????
g(1,1)g0(1,1) g1(1,1) g2(1,1)
g3(1,1)1011
g(1,2)g0(1,2) g1(1,2) g2(1,2)
g3(1,2)1111
g(1,1)?????? l ?,???1??? Cl(1) ????? l ??????
ml(1) ???????????? ml-2(1) ??????? ml-3(1)
???????2????
g(1,2)??Cl(2) ?? ml(1)?ml-1(1)?ml-2(1)?ml-3(1)
??2??
???? g(i,j) ??,???????????????g(1,1)?g(1,2)?(2,1,3
)?????????

6
7.1 ????????

? l ??????????
???????????????????????????????????????????????

7
7.1 ????????

?Mm0(1) m1(1) m2(1) m3(1)1011,??????????????
?
?????????,?????????? (k1),??????2? (n2)
?????????,??????
?????????????????????,????? m ? (m3) ?????????

8
7.1 ????????

m????(?? m3)?
Nm1????????????????????????(??N4)?
N?n???????????????????????(??N?n8)?
???????,???? C ???????????????

9
7.1 ????????

?7.2 (3,2,1)?
n3, k2, m1
???????3??????????????2????????????????2?????2????
??
????????2?????? n?(m1)326 ?????
n?k?(m1)32212??? ???,????????2?????6?????
?
g(1,1)g0(1,1) g1(1,1)11
g(1,2)g0(1,2) g1(1,2)01
g(1,3)g0(1,3) g1(1,3)11
g(2,1)g0(2,1) g1(2,1)01
g(2,2)g0(2,2) g1(2,2)10
g(2,3)g0(2,3)
g1(2,3)10 (9.1)

10
7.1 ????????

?????????
Mm0(1)m0(2) m1(1)m1(2) ml(1)ml(2)
???? C ???????

11
7.1 ????????

g(1,1)g0(1,1) g1(1,1)11 g(2,1)g0(2,1)
g1(2,1)01
g(1,2)g0(1,2) g1(1,2)01 g(2,2)g0(2,2)
g1(2,2)10
g(1,3)g0(1,3) g1(1,3)11 g(2,3)g0(2,3)
g1(2,3)10

12
7.1 ????????

??????????? k2????,??????????????2?????? (9.1)
?????????????,????1,2,3???????????3????
???? N2 ?????????2?????,?????????? k2
??????,???????????? (9.2) ?????????2?????
???????????????

13
7.1 ????????

??(n,k,m) ???? (n?k) ????????,????????? (N m1)
???????CC0(1)C0(2)C0(n)C1(1)C1(2)C1(n)Cl(1)Cl
(2)Cl(n)
???????????????Mm0(1)m0(2)m0(k)m1(1)m1(2)m
1(k)ml(1)ml(2)ml(k)
?????????

14
7.1 ????????

(2) ?????????
??????????????????????? Cl,??? n ???,?? k
???????????? l ??? ml(i) ??,?? (n-k) ???????????
?????? k ?????????? k ????,??????? g(i,j) ??
(k?k) ?????????,?

15
7.1 ????????

?? k?(n-k) ?????????,????????? (n-k) ?????

16
7.1 ????????

?????????
????????? N ?,?????? (n-k) ??????????????

17
7.1 ????????

?7.3 (3,1,2)?????
g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(1,2)g0(1,2) g1(1,2) g2(1,2)110
g(1,3)g0(1,3) g1(1,3) g2(1,3)101

18
7.1 ????????

???????

19
7.1 ????????

?7.4 (3,2,2)?????
g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(1,2)g0(1,2) g1(1,2) g2(1,2)000
g(1,3)g0(1,3) g1(1,3) g2(1,3)101
g(2,1)g0(2,1) g1(2,1) g2(2,1)000
g(2,2)g0(2,2) g1(2,2) g2(2,2)100
g(2,3)g0(2,3) g1(2,3) g2(2,3)110
??????? Cl ????? ml(1)?ml(2) ??,????????? (7.4)
??,?

20
7.1 ????????

g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(2,1)g0(2,1) g1(2,1) g2(2,1)000
g(1,2)g0(1,2) g1(1,2) g2(1,2)000
g(2,2)g0(2,2) g1(2,2) g2(2,2)100
g(1,3)g0(1,3) g1(1,3) g2(1,3)101
g(2,3)g0(2,3) g1(2,3) g2(2,3)110

21
7.2 ??????

(1) ??????????????
(2) (n-k)?m ???????????????
(??????)
(3) k?m ??????????(??????)
(4) ??

22
7.2 ??????

(1) ??????????????
??????????(9.3)???????????
?9.5?(n,k,m)?????????????

23
7.2 ??????
24
7.2 ??????

?????????(9.4)?????????
?9.6? (n,k,m) ????????????

25
7.2 ??????
26
7.2 ??????

(2) (n-k)?m ???????????????(??????)
??????????????,??????????(9.4)?????????(9.5)?
?(9.5)??????????,????? l ???? (n-k) ????,??
(n-k) ???????,???????????? m ?
???????? g(i,j) ?????????? l ???????? m ?????

27
7.2 ??????
28
7.2 ??????

?7.5 (3,2,2)???????
??????
g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(1,2)g0(1,2) g1(1,2) g2(1,2)000
g(1,3)g0(1,3) g1(1,3) g2(1,3)101
g(2,1)g0(2,1) g1(2,1) g2(2,1)000
g(2,2)g0(2,2) g1(2,2) g2(2,2)100
g(2,3)g0(2,3) g1(2,3) g2(2,3)110
???(9.5),? l ????????
Cl(3)ml(1)g0(1,3) ml(2)g0(2,3)
ml-1(1)g1(1,3)
ml-1(2)g1(2,3)
ml-2(1)g2(1,3)
ml-2(2)g2(2,3)

29
7.2 ??????

????????????
Cl(3)ml(1) ml(2) ml-1(2) ml-2(1)
(3,2,2)??????????9.7???
?9.8?(n,k,m)??????????

30
7.2 ??????
31
7.2 ??????

(3) k?m ??????????(??????)
??(9.4)?????????(9.6)?
?(9.6)?????? l ??? k ?????? m ???????????????????
?2??,????????? (n-k) ?????
??????? k ?????????,???? m ??????????????? m
????????????? k ?????

32
7.2 ??????

?7.6 (3,1,2)?,???????
g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(1,2)g0(1,2) g1(1,2) g2(1,2)000
g(1,3)g0(1,3) g1(1,3) g2(1,3)101
??(9.6),???????????
Cl(2)ml(1)g0(1,2)ml-1(1)g1(1,2)ml-2(1)g2(1,2)m
l(1)ml-1(1)
Cl(3)ml(1)g0(1,3)ml-1(1)g1(1,3)ml-2(1)g2(1,3)
ml(1)ml-2(1)
???????9.9???

33
7.2 ??????

?7.7 (3,2,2)?,?????????
g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(1,2)g0(1,2) g1(1,2) g2(1,2)000
g(1,3)g0(1,3) g1(1,3) g2(1,3)101
g(2,1)g0(2,1) g1(2,1) g2(2,1)000
g(2,2)g0(2,2) g1(2,2) g2(2,2)100
g(2,3)g0(2,3) g1(2,3) g2(2,3)110
??(9.6),???????????
Cl(3) ml(1)g0(1,3)ml-1(1)g1(1,3)ml-2(1)g2(1,3)
ml(2)g0(2,3)ml-1(2)g1(2,3)ml-2(2)g2
(2,3)
ml(1)ml-2(1)ml(2)
ml-1(2)
???????9.10???
?9.11????(n,k,m)?????????

34
7.2 ??????

Cl(3)ml(1)ml-2(1)ml(2)ml-1(2)

35
7.2 ??????
36
7.2 ??????

(4) ??
????????????????
???????????,???????????,????????????
??????,?(n-k)ltk,???????????????
??,??????????

37
7.3 ????????

???????????,?????????????????????????????????????
??????????????
????????????????????????
?????????????????????????????????
(1) ????????
(2) ????????

38
7.3 ????????

(1) ????????
?9.8 ? (2,1,3) ?????????????????
g(1,1)g0(1,1) g1(1,1) g2(1,1) g3(1,1)1011
g(1,2)g0(1,2) g1(1,2) g2(1,2) g3(1,2)1111

39
7.3 ????????

40
7.3 ????????

??????????,??
? C8TG8TM8T(M8G8) T
?? C8M8G8

41
7.3 ????????
42
7.3 ????????
43
7.3 ????????

??????G8G8 ?? (2,1,3) ???????
????????????????????,???????????, G8
?????????,?????C8????????
??(9.7)????,????G8?,????? G0G1G2G3????,???? G8
??????
??????g8 ????G8???????????????
(2,1,3)???????? g8?
g8 G0G1G2G3 00
g8 ???????????????? g(i,j) ???????
????????? C8 ??????????
(2,1,3)????????????? G0,G1,G2,G3 ?? (12)???
(k?n, k1,n2),??????4? (m1N4)?

44
7.3 ????????

?7.9 (3,2,2)?????????6??????
g(1,1)g0(1,1) g1(1,1) g2(1,1)110
g(1,2)g0(1,2) g1(1,2) g2(1,2)010
g(1,3)g0(1,3) g1(1,3) g2(1,3)100
g(2,1)g0(2,1) g1(2,1) g2(2,1)001
g(2,2)g0(2,2) g1(2,2) g2(2,2)100
g(2,3)g0(2,3) g1(2,3) g2(2,3)111
?????
Mm0(1)m0(2)m1(1)m1(2)m2(1)m2(2)m3(1)m3(2)
?? (9.3),?????? C ?

45
(No Transcript)
46
7.3 ????????

??????,???(3,2,2)?????????????

47
7.3 ????????

(n,k,m) ?????????????

48
7.3 ????????

??????C?????????0,?????Nm1????,?N?k?????,??????
?Nm1???,?N?n???,??Nm1?????????????????????
CC0C1C2Cm
?? CiCi(1)Ci(2) Ci(n) i0,1,2, m
??????????? C MG
??Mm0m1m2mm
mimi(1)mi(2) mi(k)
i0,1,2, m

49
7.3 ????????

??????????? G
?????? g
g G0G1G2Gm

50
7.3 ????????

??????????
(kk) ?????????,??
ij?,g(i,j)1?i?j?, g(i,j)0,i1,2,,kj1,2,,k?

??????? k ??????? k ???????(n-k)?????????????????
?????
??????????????????

51
7.3 ????????

?? Ik ? k ?????
Pl? k(n-k) ??,l0,1,2,,m
???????????????????
g IkP0 0P1 0P2 0Pm
????????????????????????????????,?????,???????????
??????????

52
7.3 ????????

(2) ????????(?????????????)
???????????????????? (n-k) ???????,?????????? m
???????????????????????,???????????
?9.10 (3,1,2)?????
g(1,1)g0(1,1) g1(1,1) g2(1,1)100
g(1,2)g0(1,2) g1(1,2) g2(1,2)110
g(1,3)g0(1,3) g1(1,3) g2(1,3)101

53
7.3 ????????