1、1?1.3:n?1?HO?5“1?2,3?1?:2?111?a11a12a21a22?=a11a22 a12a21.l 2?1?Lw 2!=2?.z5g1?.1 a11a22,1I:g,S?;?I:?1?a12a21,1I:g,S?;?I:?K5“1?2,3?1?:3?111?a11a12a13a21a22a23a31a32a33?=a11a22a33+a12a23a31+a13a21a32a13a22a31 a12a21a33 a11a23a32.l 3?1?Lw 3!=6?.z5g1?n?.z1IUg,S;?ITA?k?3?;?123 231 312?321 213 132K5“1?22e
2、?,?.l 3?u 3?1?z/X()a1j1a2j2a3j3.j1j2j3A?3?(j1j2j3)?(j1j2j3)Ku(1)(j1j2j3)5LT?3?1?z/X(1)(j1j2j3)a1j1a2j2a3j3.3?1?L?a11a12a13a21a22a23a31a32a33?=Xj1j2j3(1)(j1j2j3)a1j1a2j2a3j3.5“1?1?n?111?:n?1?a11a12a1na21a22a2n.an1an2ann?n!?;zd5g1?n?;rz n?U1Ig,S?,?IA?n?:(1)?,TK;(2)?,T?.=?a11a12a1na21a22a2n.an1an2ann?=
3、|(aij)nn|=Xj1j2jn(1)(j1j2jn)a1j1a2j2anjn.j1j2jnL n?,Xj1j2jnLk n?.5“1?1?O 1,2,3?N.555 4?111?vvvkkk?KKK.DDD111?999AAA111?1O1?0010000203004000?.2O?,B?1?:D1=?a11000a220.00ann?;D2=?00a1n0a2(n1)0.an100?D1=a11a22ann;D2=(1)n(n1)2a1na2(n1)an1,D2c?K.5“1?1?O3en?1?:D3=?a110a22.00ann?;D4=?a1100a220.ann?D3=a11a22
4、ann=D4.5“1?1?1?IS?(?a11a12a1na21a22a2n.an1an2ann?=Xj1j2jn(1)(j1j2jn)a1j1a2j2anjn.31?n?7LU1Ig,S.?k?,dU?gS?n?.TXNyTc?Q?(1)(j1j2jn)a1j1a2j2anjn(?)ai1k1ai2k2ainkn5“1?1?1?IS?(1)(j1j2jn)a1j1a2j2anjn(?)ai1k1ai2k2ainkn?a1j1a2j2anjn s gC ai1k1ai2k2ainjn.O51?I:1I:1,2,nsg i1i2in;?I:j1,j2,jnsg k1k2kn.5?UC?5(1)s
5、=(1)(12n)(1)s=(1)(i1i2in)(1)(j1j2jn)(1)s=(1)(k1k2kn)s (i1i2in)5.(j1j2jn)+s (k1k2kn)5.5“1?1?1?IS?(u(1)(j1j2jn)=(1)s(1)(j1j2jn)(1)s=(1)s(1)(k1k2kn)=(1)(i1i2in)+(j1j2jn).l?(1)(j1j2jn)a1j1a2j2anjn=(1)(i1i2in)+(k1k2kn)ai1k1ai2k2ainkn?1?i1i2in,K n?1?|aij|=Xj1j2jn(1)(i1i2in)+(j1j2jn)ai1j1ai2j2ainjn?j1j2jn,
6、K n?1?|aij|=Xi1i2in(1)(i1i2in)+(j1j2jn)ai1j1ai2j2ainjn5“1?1?U?Ig,S?AO/,?I?g,S?,=?|aij|=Xi1i2in(1)(i1i2in)ai11ai22ainn.5“1?51.4:1?5HO?5“1?5O1?(J 3!,?n?1?m,|O?A/G1?.?N?y1?X n?O4/O:X5!=120;10!=3628800.e,O1?O,N?y.!l1?u1?5,|1?5z1?O.5“1?51?=1?D?1?p?#1?1?=(transpose),P DT.=D=?a11a12a1na21a22a2n.an1an2ann?=
7、DT=?a11a21an1a12a22an2.a1na2nann?PD=|(aij)nn|=DT=|(bij)nn|bij=aji.5“1?5=1?51 1?=1?,=?a11a12a1na21a22a2n.an1an2ann?=?a11a21an1a12a22an2.a1na2nann?(D=DT).yyy?D=|(aij)nn|,K DT=|(bij)nn|bij=aji.DT n?1?U?Ig,S?DT=Xi1i2in(1)(i1i2in)bi11bi22binn.5?bij=aji,uDT=Xi1i2in(1)(i1i2in)a1i1a2i2anin=D.5“1?51?1?=y?1?1
8、?p.5 1 L1?1?/?.d1?k1?5,u?.8?1?k1?5.g1u1?5k?5.5“1?51?5 252 1?1?fJ?,=?a11a12a1n.kai1kai2kain.an1an2ann?=k?a11a12a1n.ai1ai2ain.an1an2ann?.yyy=Xj1j2jn(1)(j1j2jn)a1j1(kaiji)anjn=kXj1j2jn(1)(j1j2jn)a1j1aijianjn=m5“1?5?k=0,=?XJ1?k1?,K1?0.555 3?a11a12a1n.b1+c1b2+c2bn+cn.an1an2ann?1 i 1=?a11a12a1n.b1b2bn.an1
9、an2ann?+?a11a12a1n.c1c2cn.an1an2ann?.5“1?5yyy=Xj1j2jn(1)(j1j2jn)a1j1(bji+cji)anjn=Xj1j2jn(1)(j1j2jn)a1j1bjianjn+Xj1j2jn(1)(j1j2jn)a1j1cjianjn=m.555?a1+a2b1+b2c1+c2d1+d2?6=?a1b1c1d1?+?a2b2c2d2?(JA=?a1b1c1d1?+?a1b2c1d2?+?a2b1c2d1?+?a2b2c2d2?5“1?554 1p1?,=?a11a12a1n.ai1ai2ain.ak1ak2akn.an1an2ann?=?a11a
10、12a1n.ak1ak2akn.ai1ai2ain.an1an2ann?1 i 11 k 1yyy5?m?1?1 i 1?1I k 1 k 1?1I i.d1?m=1 Xj1jijkjn(1)(j1jijkjn)a1j1(akji)i(aijk)kanjn5“1?5m=1 Xj1jijkjn(1)(j1jijkjn)a1j1(akji)i(aijk)kanjn=1Xj1jkjijn1 (1)(j1jkjijn)a1j1(aijk)i(akji)kanjn=Xj1jkjijn(1)(j1jkjijn)a1j1aijkakjianjn=55 1,1?0.56 1,1?0.5“1?5?,yyyy n
11、?.yyy?11111111.1111?=0=Xj1j2jn(1)(j1j2jn)1n=?k n!,z?(JU 1 1.u?K,1?.PPP1 i 1(?)1 j 1(?)?P ri rj(ci cj).5“1?557 1?,1,1?C,=?a11a12a1n.ai1ai2ain.ak1+ai1ak2+ai2akn+ain.an1an2ann?=?a11a12a1n.ai1ai2ain.ak1ak2akn.an1an2ann?yyyd5 3 95 2?5“1?5=?a11a12a1n.ai1ai2ain.ak1ak2akn.an1an2ann?+?a11a12a1n.ai1ai2ain.ai1
12、ai2ain.an1an2ann?=?a11a12a1n.ai1ai2ain.ak1ak2akn.an1an2ann?=m5“1?51?O?PPP1 i 1(?)?1 k 1(?)P rk+ri(ck+ci)c?1?u1?5u?.g1Q.?5 7 5 4.1?L57,4 ()n?1?(?)53,?K?U?-.5“1?5SOe?1?,(1)?231503201298523?;)?=?231500+3200+13002523?=?231500200300523?+?231312523?=?231312523?=?141312523?=?14101110188?=?11401110818?=?114
13、01110070?=70.5“1?5S(2)?abbbbabb.bbba?(ab.)?=?a+(n1)bbbba+(n1)babb.a+(n1)bbba?=(a+(n1)b)?1bbb1abb.1bba?=(a+(n1)b)?1bbb0ab00.000ab?=(a+(n1)b)(ab)n1.5“1?5S(3)?3112513420111533?;)?=?1312153402115133?=?13120846021101627?=2?13120211042301627?=2?131202110045001015?5“1?5S?=2?131202110045001015?=2?132102110054001510?=2?1321021100540002?=212 52=40.5“1?5S(4)?a1+b1a1+b2a1+b3a2+b1a2+b2a2+b3a3+b1a3+b2a3+b3?)3?1?z?|?,o?8 1?,z1?le 4|?3()|?:a1b1b2b3a2b1b2b3a3b1b2b3du2,3|,2,4|,3,4|,8 1?k?k?.l?0.dd?1?0.5“