搜索
(20):1.xRnzRn(n1),nQQx=|x|z.()2.HmmHouseholder,In-mn-m(mn),Hn=HmOOIn-mnHouseholder.()3.A=diag(1,2,,n),mB1,2,,n,(m1),AB().4.Amn,BnmCmm,AXB=C().5.A=110001000,A(1,2)=.6.A=14-1-1-30001,AJordanJ=.(10):CnnmF.(12)A=3083-16-20-5,x(0)=111.1.eAt.2.ddtx(t)=Ax(t)x(0).(:eAt)(12)GivensA=355034405QR.(12)GerschgorinA=205141011210i(i=-1),.(12)A=101011112,b=111.1.A.2.A+.3.Ax=bx0(x0).(12)R22,B=0140,T:TX=XB(XR22).R22,T.(10)Vnx1,x2,,xnA,:Vny1,y2,,yn,(xi,yj)=1(i=j)0(ij)6611..QHouseholder,Givens.2..Hm=In-2umuTm(|um|=1),Hn=ImOOIn-m-2umuTmOOO=In-2um0uTm0Tvn=um0,vTnvn=uTmum=1,|vn|=1,Hn=In-2vnvTnHouseholder.3.ABij,1,,m,21,,2m,,n1,,nm.4.AA(1)CB(1)B=C,vec(C)R(ABT).5.P=(e1,e3,e2),A(1,2)=P100010000=1000000106.det(I-A)=(-1)(+1)2,rank((-1)I-A)=2,(+1)23-2=1.A(-1),(+1)2,J=1-11-1A=(aij)nn,Am=nmaxi,j|aij|,AF=ni,j=1|aij|212761Am=n[maxi,j|aij|2]12n[ni,j=1|aij|2]12=nAFAF[n2maxi,j|aij|2]12=nmaxi,j|aij|=Am1AFAmnAF,AmAF.det(I-A)=(+1)3,A+IO,(A+I)2=O,Am()=(+1)2.f()=et=m()g()+(a+b),f()=tet=[mg]+b,f(-1)=e-t=a-bf(-1)=e-t=ba=(t+1)e-tb=te-teAt=aI+bA=e-t[(1+t)I+tA]=e-t1+4t08t3t16t-2t01-4tx(t)=eAtx(0)=e-t1+12t1+9t1-6t1=(3,0,4)T,T13(c,s):c=35s=45,T1=T13=15304050-403,T1A=5370340-4-1A1=34-4-1,2=3-4T12(c,s):c=35,s=-45,T2=T12=153-443,T2A1=51650135861T=1T2T1,Q=TT=1251516-120152020-129R=5375165135,A=QRD=diag(1,1,3),B=DAD-13A.1.A101011000,A=100111101011=FG2.F+=(FTF)-1FT=2112-1FT=132-11-121G+=(FT)+=(F+)T=132-1-1211A+=G+F+=195-41-4511123.x0=A+b=19224,AA+b=23112b,x0.R22E11,E12,E21,E22,TE11=E11B=0100=0E11+1E12+0E21+0E22961TE12=E12B=4000=4E11+0E12+0E21+0E22TE21=E21B=0001=0E11+0E12+0E21+1E22TE22=E22B=0040=0E11+0E12+4E21+0E22,TA=0400100000040010P-1AP=,=22-2-2,P=202010-100202010-1(X1,X2,X3,X4)=(E11,E12,E21,E22)PX1=2100,X2=0021X3=2-100,X4=002-1TX1,X2,X3,X4.A=(aij)nn,C=(cij)nn,(y1,,yn)=(x1,,xn)C,yj=c1jx1++cnjxn(xi,yj)=c1j(xi,x1)++cnj(xi,xn)=ai1c1j++aincnjI=(x1,y1)(x1,yn)(xn,y1)(xn,yn)=AC071A,C=A-1.,y1,,yn,(y1,,yn)=(x1,,xn)A-1.(20):1.nA,cosA.()2.TmmGivens,In-mn-m(mn),Tn=TmOOIn-mnGivens.()3.ARnn1,2,,n,AT=A.BRnnA,B().4.ACnnA+,B=AA,B+=.5.R2e1=10,e2=01,=11,L=L(),PL=.6.A=010-120-110,AJordanJ=.(10):Cnnm1Cnp(p1).(:A=(aij)nn=ni=1nj=1aijEij)171(12)A=0100000000000000001100001,b(t)=2t0000.1.eAt.2.ddtx(t)=Ax(t)+b(t)x(0)=(1,1,1,1,1)T.(12)HouseholderA=3149643362215QR.(12)GerschgorinA=2061181283i(i=-1),.(12)A=100111,b=112.1.A.2.AA+.3.Ax=bx0(x0).(12)P2[t]f1(t)=1-t,f2(t)=1+t2,f3(t)=t+2t2TTf1(t)=2+t2,Tf2(t)=t,Tf3(t)=1+t+t21.T.2712.f(t)=1+2t+3t2,Tf(t).(10)Vn1,2,,n,0=1+22++nn,T=+k(,0)0(Vn,k)1.T.2.Tk=-212+22++n2.1..A=O,cosA=I.2..3.(B)=(A)=(ATA)=(A2)=|(A)|,B|1|,|2|,,|n|.4.AO,AA=FG,B=FGFG=FFG=FGF+=[FHFH]FF-1[FHFH]=12(FHF)-1[FHFH]=12[F+F+]B+=G+F+=G+12[F+F+]=12[A+A+]A=O,.5.PL=(T)-1T=121111.6.det(I-A)=(-1)2.rank(1I-A)=2,(-1)23-2=1.A,(-1)2,371J=0111A=(aij)nn,x=(1,2,,n)T,Ax=ni,j=1aijEijxEijx=jei,Eijxp=[|j|p]1pxpAxpni,j=1|aij|Eijxpni,j=1|aij|xp=Am1xpAm1xp.J1=0100,J2=0,J3=1101,A=J1J2J3eAt=eJ1teJ2teJ3t=1t11ettetetx(t)=eAtx(0)+t0e-Asb(s)ds=eAt11111+t20000=1+t+t211(1+t)etet4711-|1|e1=366-9100=6-111,u1=13-111H1=I-2u1uT1=1312221-22-21H1A=9481509-30-129,A1=9-3-1292-|2|e1=9-12-1510=-612,u2=1512H2=I-2u2uT2=153-4-4-3,H2A1=15-90-3Q=H11H2=155-2-141011210-105R=9481515-9-3,A=QRA=diag(1,1,0.5),B=DAD-13A.1.B=ATA=2112,det(I-B)=(-3)(-1).1=3,p1=11;2=1,p2=1-1=3001,V=12111-1rankA=2V1=V,571U1=AV1-1=161216-12260,U2=1313-13U=[U1U2]=16121316-1213260-13A=U300100VT2.A+=V1300010UT=132-11-1213.x0=A+b=11,AA+b=112=b,x0.1.(f1,f2,f3)=(1,t,t2)110-102012=(1,t,t2)B1(Tf1,Tf2,Tf3)=(1,t,t2)201011101=(1,t,t2)B2T(f1,f2,f3)=(f1,f2,f3)B-11B2,T671A=B-11B2=-1-2-2323-1-1-12.f=(1,t,t2)123=(f1,f2,f3)B-11123=(f1,f2,f3)-230Tf=(f1,f2,f3)A-230=(f1,f2,f3)-40-1=-4+3t-2t21.,Vn,l1,l2R,T(l1+l2)=(l1+l2)+k(l1+l2,0)0=l1[+k(,0)0]+l2[+k(,0)0]=l1(T)+l2(T)T.2.T(T,T)=(,)(Vn),(,)+2k(,0)2+k2(,0)2(0,0)=(,)k(,0)2[2+k(0,0)]=0Vn,2+k(0,0)=0,k=-2(0,0)=-212+22++n2(15):1.AnHouseholder,cos(2A)=().2.x=(1,2,,n),1p+,x=()xp=().3.AmmBnn,(AHB)(ABH)=().7714.X=111213212223,f(X)=11+212+313,dfdX=.5.A=111010001,AJordanJ=.(12)A=(aij)mn,AG=mnmaxi,j|aij|:AGCmn,2-.(12)A=100-101-100-110-1001.1.eAt.2.ddtx(t)=Ax(t)x(0)=(1,0,0-1)T.(12)HouseholderA=03104-2212QR.(12)GerschgorinA=9017180815240(),.(13)A=-112-221-1-2011-2,b=00154.8711.A.2.A+.3.Ax=b.4.Ax=bx0().(12)R22,P=1021,T:TX=PXP-1(XR22)1.T.2.T.(12)Vnx1,x2,,xn,x,yVn(1,2,,n)T(1,2,,n)T,(x,y)=11+22++nn,:1.(x,y)Vn.2.,x1,x2,,xnVn.1.AHouseholder,A2=I,cos(2A)=I-12!(2A)2+14!(2A)4-=1-(2)22!+(2)44!-I=[cos(2)]I=I2.max1in|i|,ni=1|i|p1p.3.(AHB)(ABH)=(AHA)(BBH)=ImIn=I(mn)4.121232130009715.det(I-A)=(-1)3.rank(1I-A)=1,(-1)33-1=2,A(-1)2,(-1),J=1111:A=O,aij=0,maxi,j|aij|=0,AG=0;AO,ai0j00,AG=mnmaxi,j|aij|mn|ai0j0|0..:B=(bij)np,ABG=mpmaxi,jnk=1aikbkjmpmaxi,j[nk=1|aik||bkj|]mpnmaxi,j|aij|maxi,j|bij|=[mnmaxi,j|aij|][npmaxi,j|bij|]=AGBG,AG.x=(1,2,,n)T,Ax22=mi=1nj=1aijj2mi=1[nj=1|aij||j|]2mi=1[(nj=1|aij|2)(nj=1|j|2)]=[mi=1nj=1|aij|2][nj=1|j|2][(mn)maxi,j|aij|2]x22=A2Gx22Ax2AGx2.081A,P-1AP=,=0022,P=1001011001-10100-1,P-1=12PeAt=P11e2te2tP-1=P1100P-1+e2tP0011P-1=121001011001101001+et2100-101-100-110-1001=121+e2t001-e2t01+e2t1-e2t001-e2t1+e2t01-e2t001+e2tx(t)=eAtx(0)=(e2