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1、C273C4t"℄a/~sYVol.27,No.42007n11JOURNALOFMATHEMATICALRESEARCHANDEXPOSITIONNov.,2007u6G:1000-341X(2007)04-0697-07f7℄XARws4:e`z>Epr112,,(1.oU6!FoUf150080;2.$E6!})8th$410076)(E-mail:x.m.tang@163.com)tj:&&2m EEb{2??dSY)),k)),=wH;Y)
2、}2y?.7^`AY)qS)i4?xY)F;:2mY)B1Y),42MSC(2000):15A04;51D20yaBT:O151.21ni1luZ[X%m76/>fX_-+7 l 8W[[1,2][3]RaFw"dqt. 1ltz“X(A0”>_-Wa'.X(A01W_-fXV}>+gwm>_-F%d>[4].(g + aE)>X(++m℄6h!>(+72X([5]+_-“(A0”.
3、qt1lDD%4XXj(A01GH'1lDD rZ+#RlDD>Xqt-x(1:>(+-6℄h_pR>X(+>X(+∗∗DfX-xFfXDFVDF>U'hMm×n(D)TDm×n1;m=ny=Mm(D).hArank(A)V1A>(T=−AeF1A[0AyA>'
4、=0,%A=31Fm"31n=Km(F).zhGLn(D
5、)D>n"fX~*w>n":l5">1'℄&>~EijDnBiWBj'1u+'0>1u"7G:yhInn"9?;i6、Bwo=Km(F)1>=o*hA,B∈Km(F)yrank(A−B)=2,%A
7、BKm(F)wϕ1Mm×n(D)(~Km(F))<->sÆevA
8、Bw:9+ϕ(A)
9、ϕ(B)w[2,6]%ϕwG>DD1.1DD1.2V=vuZ[ <ÆHb>#R1l[7]
10、DDhvSeAb>31lDD[2,6]−1?U1.1m,n=5z1>ϕ1Mm×n(D)<->#Æeϕ
11、ϕFw;m6=nϕ=GV)ϕ([aij])=P[f(aij)]Q+R,∀[aij]∈Mm×n(D),^C[:2005-12-05;_[:2006-08-26hZ:d/9^((10671026);pV 49g(11521217).698!`.}rX273uP∈GLm(D),Q∈GLn(D),R∈Mm×n(D),f=D>fX-6℄;m=n-aV):ϕz:kwhGV)ϕ(
12、[a])=P[g(a)]TQ+R,∀[a]∈M(D),ijijijm×n−1uP,Q,R>ln6g=D>fX-6℄V>ϕ5#Æyϕϕ5w[7]−1?U1.2m=5z3>ϕ1Km(F)<->#Æeϕ
13、ϕFw;n>4ϕ=hGV)>{ϕ([a])=αPT[f(a)]P+R,∀[a]∈K(F),ijijijm∗uα∈F,P∈GLm(F),R∈Km(F),fF>fX-6℄;m=4ϕ=hGV)T∗ϕ([aij])=αPf([aij])P+R,∀[aij]∈Km(F),∗uuα,P,R,f>
14、ln6[aij]7−→[aij]~=qsÆ~=hGsÆ0a12a13a140a12a13a23−a120a23a24−a120a14a247−→.−a13−a230a34−a13−a140a34−a14−a24−a340−a23−a24−a340−1V>sÆ5#Æyϕϕ5w29AvH5V=Doqϕ1Mm×n(D)<->sÆe*w>A,B∈Mm×n(D)Fwϕ(A+B)=ϕ(A)+ϕ(B),%ϕ=Mm×n(D)>(+yevrank(A+B)=rank(A)+ran
15、k(B):9+rank(ϕ(A)+ϕ(B))=rank(ϕ(A))+rank(ϕ(B)),%ϕ=:>C&:Dn:>(+?U2.1m,n=5z1>ϕ=Mm×n