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1、SNJ;.KHome PageI K JJIIJI11 ?23 w 4555| SSSKKK()Zuo LiancuiCollege of Mathematical Science, Tianjin Normal UniversityNov. 10, 2009SNJ;.KHome PageI K JJIIJI12 ?23 w 4Main Contents1. SNJ 2. ;.KSNJ;.KHome PageI K JJIIJI13 ?23 w 41SNJ1. ?n1 3g5| a11x1+ a12x2+ + a1nxn= 0, a21x1+ a22x2+ + a2nxn= 0,. as1x1
2、+ as2x2+ + asnxn= 0,es 1. K,a16= 0,16= 0,a11= 0 g .o(1)Ca11+ + ai1i1+ aii= 0.ai6= 0,i= a1ai1 ai1 aii1,=id1, ,i15L.e3id1, ,i15L,?,1, 2, , i1, i5,l 1, 2, , i1, i, ,s5.SNJ;.KHome PageI K JJIIJI17 ?23 w 4n2 1,2, ,r1,2, ,s |,XJ (1) |1,2, ,rd1,2, ,s5 L, (2) r s, K|1,2, ,r75.1XJ|1,2, ,rd |1,2, ,s5L, 1,2, ,
3、r5 ,or s.2 ?n + 1n1,2, ,n,n+17 5.3 5d|,7k .SNJ;.KHome PageI K JJIIJI18 ?23 w 45. 45|1,2, ,s |i1,i2, ,ir45 |, XJ (1) |5,=i1, i2, , ir5 (2) u?j(j / i1,i2, ,ir, ek), j,i1, ,ir5, =2V5 .|4| |d0? |0.CO|4|.SNJ;.KHome PageI K JJIIJI19 ?23 w 42;.K(1) )5|.1)5|(x1+ x2+ x3+ x4= 1, x1+ x2 x3 x4= 2, x1 x2+ x3 x4=
4、 1.) A =11111 111 1 2 1 111 1!11111 002 2 1 0 202 0!11111 0 202 0 002 2 1!1 0 0 13 20 1 010 0 0 1112.SNJ;.KHome PageI K JJIIJI110 ?23 w 4dO2 5| x1 x4=3 2,x2+ x4= 0, x3+ x4=1 2. ) x1=3 2+ x4, x2= x4, x3= 12 x4,x4gd.(2) |4|2 | 1= (1,0,1,2),2= (0,1,0,1), 3= (1,0,0,1),4= (1,1,0,2)SNJ;.KHome PageI K JJII
5、JI111 ?23 w 44|.) 1,2,3,4?EA =1 0 1 10 1 0 11 0 0 02 1 1 2,A?1X1Cz1z F/ .A 1 0110 1010 0 1 10 1 101 0110 1010 0 1 10 0 1 11 0110 1010 0 1 10 0001 0000 1010 0 1 10 000SNJ;.KHome PageI K JJIIJI112 ?23 w 41 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0= B.B|1,2,3,4k4 |1,2,3, o|1,2,3,4k4 |1,2,3, = 3.(3) |5X3 XJ|(1)d|(2
6、)5L, o(1)L(2).y (1),(2)Or,t, i1, ,irj1, , jtO4|, Kd /|(1)d|(2)5L0, |i1, ,ird|j1, ,jt5L , dn21r t.SNJ;.KHome PageI K JJIIJI113 ?23 w 44 1,2, ,n|n,y1, 2, , n5?n 5L.y 1,2, ,n|n, 5. 1,2, ,nn |, K u?n5,k,1,2, ,n d1,2, ,n5L. dn2, , 1, 2, , n5, ?1, 2, , n5, l d1,2, ,n5L. u?Fn, d |1,2, ,n5L, 1,2, ,n d|1,2,
7、,n5L. d3,n = (1,2, ,n) (1,2, ,n).l 1,2, ,n5.SNJ;.KHome PageI K JJIIJI114 ?23 w 45 1= 2+ 3+ + r, 2= 1+ 3+ + r,. r= 1+ 2+ + r1. y1,2, ,r1,2, ,rk.y w,1,2, ,rd1,2, ,r5L . q 1+ 2+ + r= (r 1)(1+ 2+ + r)= (r 1)(r+ r) = (r 1)r+ (r 1)r. (r 1)r= 1+ 2+ + r1+ (2 r)r.SNJ;.KHome PageI K JJIIJI115 ?23 w 4or=1 r 11
8、+ +1 r 1r1+2 r r 1r.l rd1,2, ,r5L.ni=1 r 11+ +1 r 1i1+2 r r 1i+1 r 1i+1+ +1 r 1r, i = 1,2, ,r. 1,2, ,rd1,2, ,r5L.l d, k.SNJ;.KHome PageI K JJIIJI116 ?23 w 46 e16= 0, 2Ud15L, 3U d1,25L, K1,2,35.y 3|k1,k2,k3, k11+ k22+ k33= 0.ek36= 0, K3= k1k31k2 k32, g. k3= 0.ek26= 0,K2= k1k21, g. kk2= 0.ok11= 0. ?16
9、= 0, k1= 0.l 1,2,35.7 bd|1,2, ,r5 L, yL71, 2, , r5.SNJ;.KHome PageI K JJIIJI117 ?23 w 4y = k11+ k22+ + krr L . qek|c1,c2, ,cr, c11+ c22+ + crr= 0, K = (k1+ c1)1+ (k2+ c2)2+ + (kr+ cr)r.?L,kki= ki+ ci,i = 1,2, ,r, oci= 0 (i = 1,2, ,r). =1,2, ,r5 . ekL = k11+ + krr= l11+ + lrr, K(k1 l1)1+ + (kr lr)r=
10、0. ?1,2, ,r5,kili= 0(1 i r), =ki= li(1 i r), =L.SNJ;.KHome PageI K JJIIJI118 ?23 w 48 y|?5| *45|.y i1,i2, ,ir1,2, ,s 5 |.K ?1,2, ,s ? di1,i2, ,ir 5 L , i1,i2, ,ir4|. K, =3i(r+1),i(r+1)Udi1, i2, , ir5L, d/5(0i1, , ir, i(r+1)5.2 1,2, ,s z di1, ,ir,i(r+1) 5 L .e ,K = 4 |; K, = 3i(r+2)Udi1, ,ir,i(r+1)5L, oi1, ,ir,i(r+1),i(r+2)5. . k ?, 7U4|.SNJ;.KHome PageI K JJIIJI119 ?23 w 49 1,2, ,sr, 3?m i1,i2, ,im, yd| r+ms.y(i1,i2, ,im)=t.yi1, i2, , im4|(t
