线性代数思维导图全6页

A1BnmXnnXnnnXXn-n!n(Vandermonde)()()1A=A2()3()4()5()06()05+37()008()k()nNNN.mmap-2009-11-7-mn=0=0:A+B=B+A:A+(B+C)=(A+B)+CAA+0=0+A=AA-AA+(-A)=0klAB1A=A,0A=0k(lA)=(kl)Ak(A+B)=kA+kB(k+l)A=kA+lAnA(BC)=(AB)C(A+B)C=AC+BCC(A+B)=CA+CBk(kA)B=A(kB)0ABABE(E+A)(E+A)=E*exp(2)+2A+A*exp(2)Ak*Al=0AXA=0|A|X|A|=0|A|=0|A|=0ad-bc=0a/b=c/dkEnEAAkAk=Xn-1A=1XAAnnBAB=BA=EABA0A*XA=|A|XEABA+BnAAAX=BXA=BXAA,B.mmap-2009-11-7-+=ij(ij)i(i)1/ikj(jki)ikj=BAABABBAABBCACr0AAB=BA=E|A|0AmXnmnr(A)=mnmr(A)=n689.mmap-2009-11-8-=0k1=k2=...=ks=0nn0XOY(1)~(2)~12(1)(2)AB~~~~--~(RREF)1~~00RREF.mmap-2009-11-9-nmm,n......0b=000m=nCramer~~Ax=b=1bAr(A)=nr(A)nbA~~+Ax=b~~AAnmnAmxn~~~RREFrn-rn-rn-rAx=0==8232122.mmap-2009-11-11-nnn+1~rVnnn+11234=1A=1=0|A|=1|A|=-1.mmap-2009-11-12-