1、.?相似与合同2020.?n?x1?x2?xn?f(x1,x2,xn)=a11x21+a22x22+annx2n+2a12x1x2+2a13x1x3+2an1,nxn1xn?f=xTAx?A=a11a12a1na21a22a2n.an1an2ann,x=x1x2.xn.A?.anGn加蠿fl鎚以 tanxniimamhtanzxzttannx.hnanxitazx.xzttamx.xntauxzx.tazzxittaznxzxr.azIDtamxnxtanzhnttamjanxitlantazDX.xz.tl1379引加3ttcamintan.nlhintanti.xTAx=(x1,x2,xn
2、)a11a12a1na21a22a2n.an1an2annx1x2.xn?.?f=xTAx?A?f?.?A?f?.唯.?1.?A=1122(.(1)?f(x)=xTAx?(2)?f(x)=xTAx?.?(1)f(x)=xTAx=(x1,x2)1122(x1x2(TAX对于任何个n阶 知陈都有意义可以算得个次次函数也就是 个以型但该次型不 是对称矩阵的秋不定为run次 次函数XhXHXzzxtnXRhX2t2Xxztzixi3xXzt2Xz型的秩2it了以边炎扣对称知f对应13空nB21131to-75的秩为2.?A=)1ab2*?a+b=3?f(x1,x2)=xTAx=x21+3x1x2+2x
3、22.?“?”?.?f(x1,x2)=xTAx(A?)?f?.?A=(aij).?B=(bij)?bii=aii?bij=12(aij+aji)?B?f(x1,x2)=xTBx?B?f?.?f?B?.AaipuajiBAtAT2ton给 刘向是up1ftipix的秩不能轻易下结论f的秗为1只有为对阵时才可以.?.?f=n+i,j=1aijxixj(aij=aji)?x=Py?f?f=1y21+2y22+ny2n,?1?2?n?f?A=(aij)?.对何时为之标矩阵f对应的浙东 矩阵应为的肚A凹成河胙阴Pjppgpnp 为新矩阵都叩为对矩阵似2加时称双林 下扣姢阿阿道iwimiyy豳品交iiPA
4、P们MAP特殊标准形to相似.?2.?f(x1,x2,x3)=(x1+x2)2+(x2 x3)2+(x3+x1)2?f=y21+y22+y23.警解取徽1红101yzihtx.hr了72第减第得第三变换矩阵不可逆ffhtxzyixzxz.GG9和以灲 hityrhfzyitzyzzy.my32yiyihtzyEzlyiiitzytiixzixry.tn2yinFtEE.?.?.?x=Py?xTAx?P?A?.?A?A?.f=xTAx=yTPTAPy=yTdiag1,2,ny=1y21+2y22+ny2n.PAP川NAPI相似对化第三章若只需找标 妆形则可以只求特么.?(?)?.?1?.?.?2
5、?.?.fxxzXFbityzxziy.in以则以则yFyi.?(i)?n?A?ATA=E(?A1=AT)?A?.?A?A?.(ii)?A?A1=AT?|A|=1?1.?A?B?AB?.(iii)?P?y=Px?.A12的川翡不然 班三班AAEMiE諔2A让您对我1aiajo.itP刚定的A必AAIE1ATlAl1l.AEln4叭lN 1或1ABjlABJLABEBTABALABFEBTATABBB.EE.?3.?A?ATA=E?AT?A?E?.?A?1.A加 证设满 肞以2ADEaiNj1LANA闪肞双前2M双放之戏即从2-1双 02实中轻向吴元双0o以11姙灿th.?4.?f(x1,x2,
6、x3)=2(a1x1+a2x2+a3x3)2+(b1x1+b2x2+b3x3)2?=a1a2a3,=b1b2b3.(I)?f?2T+T?(II)?f?2y21+y22.叶剡NEXTGMtazhtsx2XMnxfbixitbzhuby-7双XXi22ftpiyx展开hn写对称 矩阵上验证法纪阵为2224ppTusfN2254piX121222itPi对称啦矩阵的特征值为210.?(I)?x=(x1,x2,x3)T?f?A?A?a1x1+a2x2+a3x3=xT=Tx,b1x1+b2x2+b3x3=xT=Tx.f(x1,x2,x3)=(II)A=2T+T?.2双化tippixX222年ffX225
7、4Bf2 22歼 512双pf222Tippi对称A22it验证A的特征值为2，1，0if0Me0双1ftpt22戏f们2222tff22Af222年ppsf222ftp.ifp觃这AreA0A系辫孔念出1 10.?A?.?A?.?n?T?1.?P?PTAP=200010000.f?x=Py?f=2y21+y22.n22万1reppinhA122ItppEr 222riff21AE2进步结合21为特征值可得VLAD 2从22第三个特征值为0.?f=xTAx?r?x=Cy?x=Pz?f=k1y21+k2y22+kry2r(ki=0)?f=1z21+2z22+rz2r(i=0),?k1?k2?kr?1?2?r?.?.CTAc秩相鹅肖rp丘兰仁 PtI通过化标将形来 弄正次惯性指数特值法配法.?5.?f(x1,x2,x3)=x21 x22+2ax1x3+4x2x3?1?a?.?f(x1,x2,x3)=x21 x22+2ax1x3+4x2x3配法yiaxjxit4xzhdxiilxiaxz.fiX2432Exit4lhaxPcxzz.BRt4们54soaE22