1、2.2:_?HO?5“_?|?,P m n?5|LAmnX=Bm1.=uy:5|?/?g3/q.g,?K:|/?q5/?g?)5)?5|Q?e5a?g?),/5|aq?“).5“aax=bAX=B a1a1(ax)=a1b“A1”“A1”(AX)=“A1”B(a1a)x=a1b(“A1”A)X=“A1”B1x=a1bEX=“A1”Bx=a1bX=“A1”B?g)L?:3u a k_?(?)a1.g,/?Amnkaq?“_?“A1”.u E 3?/aqui 1,9a1a=aa1=1,“A1”A=A“A1”=E“A1”?5.ug,/_?.5“_?A P?.e3?B?AB=BA=E,K A _?.B
2、 A?_?.e A _,K A B?.AB=BA=E=A,B?._?!f?gU5)?5|.?,J?)?#?;,52_O?.5“5 A B?/?.=B _ A B?_?.v AB=BA=E?B?b?B1,B2 A?_?,K AB1=B1A=AB2=B2A=E,uB1=B1E=B1(AB2)=(B1A)B2=EB2=B2.A?_?P A1.w,A1_(A1)1=A.P1AL?_.XBCA)A1BCBA1CBCA1Lk.5“_?5?E _ E1=E;e A,B _,6=0,Kv AB,A,A1,AT_.(AB)1=B1A1;(A1As)1=A1sA11;(An)1=(A1)n;(AT)1=(A1)T
3、;(A)1=1A1;(A1)1=A.5“?f|?_?.?A1=1002!,B1=A11=10012!.A2=cossinsincos!,A3=123231312(N).5“K?_?!?w,_.?_Q?kvkk?O?3_?cJeX?_?|1?m?X?Ke A _,K|A|6=0.yyy d AA1=E?|AA1|=|E|=1.l?|A|6=0.|A|6=0 A _?.L|A|6=0?B?AB=BA=E.5“?-A=a11a12a1na21a22a2n.an1an2ann,?E?A=A11A21An1A12A22An2.A1nA2nAnn,A?A?.N?yAA=AA=|A|E.?|A|6=0,AA
4、|A|=A|A|A=E=A1=A|A|.5“?_?nA _|A|6=0?A _,A1=A|A|n?:?_?O;_?.5“f 1?A=abcd!,?a,b,c,d vo,A _?_ A1.)?|A|=ad bc 6=0,A _.A11=d;A12=c;A21=b;A22=a.l?A1=1ad bc dbca!5“f 2?A=123231312,K A _?_ A1.)|A|=?123231312?=?123015057?=?1557?=18 6=0,?A _.A11=?3112?=5;A12=?2132?=1;A13=?2331?=7;A21=?2312?=1;A22=?1332?=7;A23=
5、?1231?=5;A31=?2331?=7;A32=?1321?=5;A33=?1223?=1;5“fduA11=5;A12=1;A13=7;A21=1;A22=7;A23=5;A31=7;A32=5;A33=1;l?A1=A|A|=118A11A21A31A12A22A32A13A23A33=118517175751Lfuy?p?5?B,?kN?(?C).5“e A,B?AB=E,K A,B _A1=B,B1=A.w|?y?_,I?y?=.5“2.1:?VgHO?5“?Vg?8U0?#a.?“L(?).13 100 100?K,e?Ok x1 x2,K?|x1+x2=1003x1+13x2=
6、100?)=(x1+x2=10083x2=200=(x1+x2=100 x2=75=(x1=25x2=75S,vk73)K?L?C?9?;5“UXe?L5L5|1?XgL?1?,1 n?XgL?1 n?.?.Xf?5|9)KLe?:11100313100!r23r1 11100083200!r238 111000175!r1r2 10250175!?x1=25,x2=75.5“o(3)L,|?X?1?$.?B,5|?X,rU?5?gSL.L5|?O2?,?X?L|?X?.X?5|?X?11313!O2?11100313100!5“e,e5|a11x1+a12x2+a1nxn=b1a21x1+a
7、22x2+a2nxn=b2am1x1+am2x2+amnxn=bmKT|?X?A=a11a12a1na21a22a2nam1am2amn;O2?A=a11a12a1nb1a21a22a2nb2am1am2amnbm.5“?Vgd P m n m 1 n?La11a12a1na21a22a2nam1am2amn P?m n.?,aijT?1 i 11 j?.555?=i1 A,B,C?L?.k/?A=(aij)mn.A(i,j)=aij.Pmn:P m 1 n?N.A11=(a)11=a.5“?e?A,B?1?,k?A?,K?,=Amn=Bpq=m=p,n=q A(i,j)=B(i,j).XXX
8、?1?;A?.5“Aa.?(?):k?,P 0mn 0;?:Ann1?;?:En=11.1?:cc.c5“Aa.?:diag(d1,d2,dn)=d1d2.dn 1?:?a1a2an?:a1a2.an5“?A=(aij)mn,B=(bij)mn P?m n?,-C=(aij+bij)mn A B 7L.K C A B?.P C=A+B.?k P,D=(kaij)mn,K D k A?.PD=kA.5“?$5u?,velK?A+B=B+A;(A+B)+C=A+(B+C);?vA+0=0+A=A;?A=(aij)mn,?(aij)mn A?K?,P A,A+(A)=(A)+A=0;?A B=A+(
9、B);k(A+B)=kA+kB;(k+)A=kA+A;(k)A=k(A);1A=A.5“?A=(aij)mn,B=(bij)np P?,-C=(cij)mp cij=ai1b1j+ai2b2j+ainbnj=Pnk=1aikbkj,i=1,2,m,j=1,2,p,K C A B?.P C=AB.555:k?U;?uuummm?111UUU;?1?u?1;?um?.AmnBnp=Cmp.?(i,j)?u?1 i 1m?1 j?A?,=AB(i,j)=nXk=1A(i,k)B(k,j)5“f 1e A=120312,B=4567!,C=0110!,AB BA;(AB)C A(BC).5“5 1(:
10、?Amn,Bnp,Cpq,K(AB)C=A(BC).yyy w,(AB)C A(BC)m q?.eyA?.(AB)C(i,j)=pXk=1AB(i,k)C(k,j)=pXk=1(nX=1A(i,)B(,k)C(k,j)=pXk=1nX=1A(i,)B(,k)C(k,j)A(BC)(i,j)=nX=1A(i,)BC(,j)=nX=1A(i,)pXk=1B(,k)C(k,j)=pXk=1nX=1A(i,)B(,k)C(k,j)=(AB)C(i,j).5“5 2?:b?e?U?1,KA(B+C)=AB+AC;(B+C)D=BD+CD.3?3?/aqui 1 3?:AmnEn=A;EmAmn=A.4?
11、v:k(AB)=(kA)B=A(kB).5“5ccc?$555?A B U?B A U;A B U B A U,?AB 6=BA.X A=111,B=?111?.uNA?,k?.e AB=BA K A B?.AmnBnp=(AB)mp;BnpAmn=(BA)nn=p=m=n.?.5“5 kkkfff=AB=0;A=0 B=0.XA=0001!,B=0100!?=?C 6=0 AC=BC;A=B.X AC BC:A=1234!,B=0325!,C=1111!5“?:Ak=AAA|zk;u k g f(x)=akxk+ak1xk1+a1x+a0,kf(A)=akAk+ak1Ak1+a1A+a0E.
12、e?(:A2=0=A=0?.XA=0100!(A+B)(A B)=A2 B2?k?m?5“?5|e5|a11x1+a12x2+a1nxn=b1a21x1+a22x2+a2nxn=b2am1x1+am2x2+amnxn=bm-A=a11a12a1na21a22a2nam1am2amn;X=x1.xn;B=b1.bmKAX=B./5|?/.5“?=?A=(aij)mn,n m?(bij)nm bij=aji A?=,P A0 AT.e AT=A,K A?.XA=123456!=AT=142536.=$?XXX(A+B)T=AT+BT;(kA)T=kAT;(AT)T=A;5“?=?A=201132!
13、,B=171423201,AT,BT,(AB)T9 BTAT.3fk(AB)T=BTAT,(u?.5“?=(AB)T=BTAT,(A1A2As)T=ATsAT2AT1.yyyb?A Pmn,B Pnp.w,(AB)T9 BTAT p m?.(AB)T(i,j)=AB(j,i)=nXk=1ajkbki;(BTAT)(i,j)=nXk=1BT(i,k)AT(k,j)=nXk=1B(k,i)A(j,k)=nXk=1bkiajk(AB)T=BTAT.5“f?B?BTB=1.-C=E 2BBTy:C?CCT=E.yyy CT=(E2BBT)T=ET(2BBT)T=E2(BT)TBT=E2BBT=C.C?
14、.qCCT=(E 2BBT)(E 2BBT)=E2 E(2BBT)2(BBT)E+4(BBT)(BBT)=E 4BBT+4B(BTB)BT=E 4BBT+4BBT=E.5“?1?A=(aij)nn n?,1?|(aij)nn|?A?1?,P|A|.1?$m?X:|AT|=|A|;|kA|=kn|A|;|AB|=|A|B|.5+?vk?,?u1?k|AB|=|A|B|=|B|A|=|BA|.e|A+B|6=|A|+|B|.5“|AB|=|A|B|kwN?f:?A=a11a12a21a22!,B=b11b12b21b22!,-D=?A0EB?=?a11a1200a21a220010b11b1201
15、b21b22?u D=|A|B|.,D=?0a12a11b11a11b12a21a220010b11b1201b21b22?5“|AB|=|A|B|kwN?f:?A=a11a12a21a22!,B=b11b12b21b22!,-D=?A0EB?=?a11a1200a21a220010b11b1201b21b22?u D=|A|B|.,D=?00a11b11+a12b21a11b12+a12b22a21a220010b11b1201b21b22?5“|AB|=|A|B|kwN?f:?A=a11a12a21a22!,B=b11b12b21b22!,-D=?A0EB?=?a11a1200a21a220010b11b1201b21b22?u D=|A|B|.,D=?00a11b11+a12b21a11b12+a12b2200a21b11+a22b21a21b12+a22b2210b11b1201b21b22?=?0ABEB?5“|AB|=|A|B|D=?0ABEB?=(1)2?AB0BE?=|AB|.l?|AB|=|A|B|.e,?A,B n?,aq/k|A|B|=?A0EB?=?0ABEB?=(1)n?AB0BE?=|AB|.5“
