海航线性代数考研基础讲义.pdf

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1、_jV@l8p1#n9hGSmFUD=

2、a

3、π(i1i2···in)nijn×nB^HnlU*(−1)a1i1a2i2···aninq,Dn1>)*i1···inB1,2,···,n1^Hπ(i1i2···in)Bi1i2···in1/n=6&412635q,1,2,3,4,5,61^H/B1+1+2+0+1+0=5,rD61tu*a14a21a32a46a53a651DSq,(−1)5=−1.2/1VBπ(i1i2···in)+π(inin−1···i2i1)=Cn/1grk7nlU*D

4、n=

5、aij

6、n×ntu*>1DS'Us
RFhnlU*Dn=

7、aij

8、n×n14iUm4j6W%1n−1lU*i+jBn4aij1l*bBMij,Aij=(−1)MijBaij1+/l*(Aij1*maijG8~maij1D
i)u[Dn1^Hn4aij8:f^H+/l*+/l*1e,BU*1tuma5mXnXnDn=aikAik=akjAkj,∀i,j=1,2,···,nk=1k=1XnXnaikAjk=akiAkj=0∀i6=jk=1k=125−131111B1.$D4=30−87,A41+A42−A4

9、3+A44mA41+A44.4−3511gFR3i~1.TU*m81
U*2Dn=Dn=

10、aij

11、n×n.2.U*1}U[}XZU*1

12、S3.U*U()1dw;/U*1@[a^H/aU*2kgG/aU*1b^U().4.U*1^U()B0,[i}U:f{sU*B0.5.U*1cf>U*1U()1n48,}H/{TsGU*w}HU*{TDn=

13、α1+β,α2,···,αn

14、=

15、α1,α2,···,αn

16、+

17、β,α2,···,αn

18、αimβtB~6.U*1n>U*1U

19、()1
n4a?^/Wc/^U()1:fn4"U*1

20、1−11x−11−11+x−1B2.Dn==1x−11−11+x−11−12xx121x1−143B3.f(x)=32x1tu*xmx1
/111xB4:$DB2003lU*aij=−aji,sD=.57$egFR1.z&;gFRa10···00a2···0Dn=........=a1a2···an....00···an2.)&;gFR200···0a100···a20......n(n−1)C2Dn=.........=(−1)2a1a2···an=(−1)na1a2···an

21、0an−1···00an0···003.CU&;gFRab···bba···bn−1Dn=........=(a+(n−1)b)(a−b)....bb···a01111011B5:D4=1101=111001···111···010···11···01B6:(1)Dn=.........=(2)Dn=.........=......11···001···14.*gFR11···1a1a2···an222QDn=a1a2···an=1≤i

22、333532435.U&;gFR^*ab0···00cab···000ca···00xn+1−xn+112Dn=............=......x1−x2000···ab000···ca2x1mx2BB^n=&@x−ax+bc=01}H=x=x,nx120sDn=(n+1)x0.5300025300B8:Dn=02530=00253000250001200121B9:D=01210=12100210006.egFRxa2a3···anb2x20···0PDn=b30x3···0=x2x3···xn(x−naibi)i=2xi.........

23、......bn00···xn4x1a2···ana1x2···anB10:Dn=.........=...a1a2···xn1+a111···111+a21···1B11:Dn=........=...···.111···1+ana1+1a2···an−1ana1a2+2···an−1an..........B12:Dn=.....=a1a2···an−1+n−1ana1a2···an−1an+n7.LaplacegFR:$An×nBnl@vBm×mBml@vCn×mBn×mlrvDm×nBm×nlrvACA00