- Akimitsu LAB. ??

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[]Rd231ddyy12y (3)y (2)y (1)x3x1x2z2z1Oz1z2d231ddyy12y (3)y (2)y (1)x0x"0x0x'0 1xi(p) = (x(p)i i) xi(p)=(x(p)i i)iy3y1y2z1z2z1 = a11y1 + a12y2 + + a1ryrz2 = a21y1 + a22y2 + + a2ryr... zm = am1y1 + am2y2 + + amryr(x1, x2, xr)(y1, y2, yr)(x(1)1 , x(1)2 , x(1)r), ,(x(N)1 , x(N)2 , x(N)r)(y(1)1 , y(1)2 , y(1)r), ,(y(N)1 , y(N)2 , y(N)r)y3y1y2z1z2z1z2...zm=a11 a1r. . . . . .am1 amry1y2......yr(x1, x2, xr)(y1, y2, yr)(x(1)1 , x(1)2 , x(1)r), ,(x(N)1 , x(N)2 , x(N)r)(y(1)1 , y(1)2 , y(1)r), ,(y(N)1 , y(N)2 , y(N)r)dz1z2y2y1z1y1(1),( )y2(1)z1= y1 y2a1 + a21=a1+ a22 2a2a1a11a2y2y1z1y1(1),( )y2(1)z1= y1 y2a1 + a21=a1+ a22 2a2a1a11a2y2y1z1y1(1),( )y2(1)z1= y1 y2a1 + a21=a1+ a22 2a2a1a11a2y1(1)a1 + y 2(1)a2y2y1z1y1(1),( )y2(1)z1= y1 y2a1 + a21=a1+ a22 2a2a1a11a2y 1(1)a1y1(1)a1 + y 2(1)a2y 2(1)a2d2N1ddyy12y (N)y (2)y (1)((d(1))2 = a21(y(1)1 )2 + a22(y(1)2 )2 + 2a1a2(y(1)1 y(1)2 )(d(p))2 = (a1y(p)1 + a2y(p)2 )2d2N1ddyy12y (N)y (2)y (1)((d(1))2 = a21(y(1)1 )2 + a22(y(1)2 )2 + 2a1a2(y(1)1 y(1)2 )(d(p))2 = (a1y(p)1 + a2y(p)2 )2(d(2))2 = a21(y(2)1 )2 + a22(y(2)2 )2 + 2a1a2(y(2)1 y(2)2 )d2N1ddyy12y (N)y (2)y (1)((d(1))2 = a21(y(1)1 )2 + a22(y(1)2 )2 + 2a1a2(y(1)1 y(1)2 )(d(p))2 = (a1y(p)1 + a2y(p)2 )2(d(2))2 = a21(y(2)1 )2 + a22(y(2)2 )2 + 2a1a2(y(2)1 y(2)2 )(d(N))2 = a21(y(N)1 )2 + a22(y(N)2 )2 + 2a1a2(y(N)1 y(N)2 )d2N1ddyy12y (N)y (2)y (1)((d(p))2 = (a1y(p)1 + a2y(p)2 )2U(a1, a2) = s11a21 + 2s12a1a2 + s22a22N N - 1 (d(1))2 = a21(y(1)1 )2 + a22(y(1)2 )2 + 2a1a2(y(1)1 y(1)2 )(d(2))2 = a21(y(2)1 )2 + a22(y(2)2 )2 + 2a1a2(y(2)1 y(2)2 )(d(N))2 = a21(y(N)1 )2 + a22(y(N)2 )2 + 2a1a2(y(N)1 y(N)2 )+d2N1ddyy12y (N)y (2)y (1)((d(1))2 = a21(y(1)1 )2 + a22(y(1)2 )2 + 2a1a2(y(1)1 y(1)2 )(d(p))2 = (a1y(p)1 + a2y(p)2 )2(d(2))2 = a21(y(2)1 )2 + a22(y(2)2 )2 + 2a1a2(y(2)1 y(2)2 )(d(N))2 = a21(y(N)1 )2 + a22(y(N)2 )2 + 2a1a2(y(N)1 y(N)2 )U(a1, a2) = a21 + 2r12a1a2 + a22+N N - 1 a21 + a22 = 1 U(a1, a2) a1 a2U(a1, a2) = s11a21 + 2s12a1a2 + s22a22a21 + a22 = 1 U(a1, a2) a1 a2G(a1, a2, ) = U(a1, a2) (a21 + a22 1)U(a1, a2) = s11a21 + 2s12a1a2 + s22a22a21 + a22 = 1 U(a1, a2) a1 a2G(a1, a2, ) = U(a1, a2) (a21 + a22 1)U(a1, a2) = s11a21 + 2s12a1a2 + s22a22a1a2 s11a1 + s12a2 a1 = 0s12a1 + s22a2 a2 = 0a21 + a22 = 1a21 + a22 = 1 U(a1, a2) a1 a2G(a1, a2, ) = U(a1, a2) (a21 + a22 1)U(a1, a2) = s11a21 + 2s12a1a2 + s22a22a1a2 s11a1 + s12a2 a1 = 0s12a1 + s22a2 a2 = 0a21 + a22 = 1(s11 s12s12 s22) (a1a2)= (a1a2)a21 + a22 = 1a21 + a22 = 1 U(a1, a2) a1 a2G(a1, a2, ) = U(a1, a2) (a21 + a22 1)U(a1, a2) = s11a21 + 2s12a1a2 + s22a22(s11 s12s12 s22) (a1a2)= (a1a2)a1a2 s11a1 + s12a2 a1 = 0s12a1 + s22a2 a2 = 0a21 + a22 = 1a21 + a22 = 1a21 + a22 = 1 U(a1, a2) a1 a2G(a1, a2, ) = U(a1, a2) (a21 + a22 1)U(a1, a2) = s11a21 + 2s12a1a2 + s22a22(s11 s12s12 s22) (a1a2)= (a1a2)a1a2 s11a1 + s12a2 a1 = 0s12a1 + s22a2 a2 = 0a21 + a22 = 1a21 + a22 = 1U(a1, a2) = a21 + 2r12a1a2 + a22a1 + r12a2 a1 = 0r12a1 + a2 a2 = 0a21 + a22 = 1a1a2 a21 + a22 = 1 U(a1, a2) a1 a2G(a1, a2, ) = U(a1, a2) (a21 + a22 1)a21 + a22 = 1(1 r12r12 1) (a1a2)= (a1a2)U(a1, a2) = a21 + a22 + 2r12a1a2= a1(a1 + r12a2) + a2(r12a1 + a2)= (a21 + a22 ) = U(a1, a2) = s11a21 + s22a22 + 2s12a1a2= a1(s11a1 + s12a2) + a2(s12a1 + s22a2)= (a21 + a22 ) = U(a1, a2) = a21 + a22 + 2r12a1a2= a1(a1 + r12a2) + a2(r12a1 + a2)= (a21 + a22 ) = U(a1, a2) = s11a21 + s22a22 + 2s12a1a2= a1(s11a1 + s12a2) + a2(s12a1 + s22a2)= (a21 + a22 ) = 12(A =s11 s12 s1rs21 s22 s2r....... . ....sr1 sr2 srr1 2 r 0i1 + 2 + + r=irk=1k1 + + i1 + 2 + + r=ij=1jrk=1kr )Aai = iai ai =ai1ai2...air (r )1 2 r 0Aai = iai ai =ai1ai2...air A =1 r12 r1rr21 1 r2r....... . ....rr1 rr2 1rri1 + 2 + + r=irk=1k1 + + i1 + 2 + + r=ij=1jrk=1kr )Aai = iai ai =ai1ai2...air z1 = a11y1 + a12y2 + + a1ryrz2 = a21y1 + a22y2 + + a2ryr... zm = am1y1 + am2y2 + + amryrm A =s11 s12 s1rs21 s22 s2r....... . ....sr1 sr2 srr1 + + m1 + 2 + + r=mj=1jrk=1kr )Aai = iai ai =ai1ai2...air z1 = a11y1 + a12y2 + + a1ryrz2 = a21y1 + a22y2 + + a2ryr... zm = am1y1 + am2y2 + + amryrm A =1 r12 r1rr21 1 r2r....... . ....rr1 rr2 1rr1 + + m1 + 2 + + r=mj=1jrk=1kRd231ddyy12y (3)y (2)y (1)R> w1 w2 summary(w2)>plot(w2$x,type=n)>text(w2$x,rownames(w2$x))R Rname height weightA1 147.3 52.3 A2 149.9 53.2 A3 152.4 54.5 A4 154.9 55.9 A5 157.5 57.3 A6 160.0 58.6 A7 162.6 60.0 A8 165.1 61.4 A9 167.6 63.2 A10 170.2 64.5 A11 172.7 66.4 A12 175.3 68.2 A13 177.8 70.0 A14 180.3 72.3 A15 182.9 74.5name height weightA01 -1.5652476 -1.4022687A02 -1.3416408 -1.2732255A03 -1.1180340 -1.0796608A04 -0.8944272 -0.8860962A05 -0.6708204 -0.6925315A06 -0.4472136 -0.4989668A07 -0.2236068 -0.3054021A08 0.0000000 -0.1118374A09 0.2236068 0.1462489A10 0.4472136 0.3398136A11 0.6708204 0.5978998A12 0.8944272 0.8559861A13 1.1180340 1.1140723A14 1.3416408 1.4366802A15 1.5652476 1.7592880R> w1 w2 summary(w2)>plot(w2$x,type=n)>text(w2$x,rownames(w2$x))RR> w1 w2 summary(w2)>plot(w2$x,type=n)>text(w2$x,rownames(w2$x))Rd231ddyy12y (3)y (2)y (1)1 r(U(a1, a2, , ar) = s11a21 + s22a22 + + srra2r+2(s12a1a2 + s13a1a3 + + sr1rar1ar)= s11a21 + s22a22 + + srra2r+( s12a1a2 + s13a1a3 + + s1r1ar1ar1 + s1rarar)+(s21a2a1 + s23a2a3 + + s2r1a2ar1 + s2ra2ar)+(sr1ara1 + sr2ara2 + sr3ara3 + + sr1rarar1 )= a1(s11a1 + s12a1 + + s1rar)+a2(s21a1 + s22a2 + + s2rar) +ar(sr1a1 + sr2a2 + + srrar)= (a21 + a22 + + a2r ) = r(r - 1)r