线性代数超强总结

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1()0ArAnAAxAA12()0,,TsinArAnAxAAAAAAAppppAxR12,,,neeenn12,,,neee12,,,1neeetr()=Enn12,,,neee.AB,(1)mnAAAABBBBAABB.(1)211212112111(1)nnnnnnnnnnnaaaaaaaaa:1AAA21()()AEEA11abdbcdcaadbcTTTTTABACCDBD12111121naanaaaa21111211naanaaaa11111221nnAAAAAA11121211nnAAAAAAmnmnAAA()()mnmnAA1110()mmmmfxaxaxaxanA1110()mmmmfAaAaAaAaEA.,,mnnsABA12,,,n,B12,,,sAB12,,,srrr,1212121122,1,2,,,(,,,)(,,,),(,,,),,,.iissTnnniiiirAisAAAAABbbbAbbbABirAABirB,,.,,11112222,kkkkABABABAB311112222kkkkABABABABAXBXAB(I)(II)0A,,BABEX(I)()()TTTTAXBXX(II)(I)AxBx,AB,,.12,,,s0Ax12,,,s12,,,s0Ax()snrA.,..,,.,,..12,,,ni(1i)n.12,,,n1n.12,,,ni1n.4m12,,,n()rAnm12,,,n()rAn.()0rAA.12,,,n12,,,,n,12,,,n,.?..?,.,.12,,,n12,,,n.1212,,,,,,nnAB.AB?AB()(),rArBAB,.AB1212(,,,)(,,,)nnrr1212(,,,,,,)nnrAB.?12,,,s12,,,n1212(,,,,,,)nsr12(,,,)nr12(,,,)sr12(,,,)nr.?12,,,s12,,,n,sn12,,,s.12,,,s,12,,,n,sn.?12,,,s12,,,n,12(,,,)sr12(,,,)nr,?.?,.?,.5?Amn,()min,rAmn,()rAmA()rAnA,12,,,n.Ax1122nnxxx1112111212222212,,nnmmmnnmaaaxbaaaxbAxaaaxb12,1,2,,jjjmjjn61212120,,,0,,,()(),,,AnAnnAxAxAnAxAxAAxrArAn12()(),,,()()()1()AnrArAAxrArArArA()TTAA()TTTABBA()TTkAkATAA()TTTABAB11()AA111()ABBA111()kAkA11AA11()()TTAA11()()kkkAAA2()nAAA()ABBA1()nkAkA1nAA11()()()()AATTAAAA()()kkAAAAAAAE()()1()10()1nrAnrArAnrAnABABnkAkAkkAA71212121211221212(1),0,(2)0,,(3),,,0,,,,,(4),0,(5),,0(6)kkkkAxAxkkAxkAxAxAxAxAx211212112212112212,0(7),,,,100kkkkkkkAxAxAxAxAxAmn,()rAm,()()rArA,Ax.mn,.,.m()()rArA.()()()TTrArArAA()rAB()()rArB()rABmin(),()rArB()0()00rAkrkAk()()ArrArBB0,()ArA1,,()0,()()mnnsABrABrArBn,()()()PQrPArAQrA,,()()ArABrB,()()BrABrA(),()(),rAnrABrBA:80ABBABACBCnn,,1.(,)0.(,)1.(,)0,(,)0(,)(,)1212(,)(,)(,)1212(,)(,)(,)(,)(,)(,)ccc123,,,112122111313233121122(,)()(,)(,)()()111222333TAAE.AAnn.1TAATTAAAAEA,TA1A1-1.AEA.9A()EAf.A0EA.AxxAxxn.0A,0A,0Ax0.12nA1niAtr()1rA,AA=1212,,,nnaabbba21122()nnAabababA,A11122nnAabababtr,230n.A12,,,n()fx,:()fA12(),(),,()nfffA,1A12111,,,n,A12,,,nAAA.1122,.mmAkkAabaAbEAAAAA:1122,mmAkkAabaAbEAxAxAAA.AB1BPAPPABAAn.,PA101PAP,A.A()iinrEAkiki.nAn,A.AB1BPAPP11AB,ABTTABkkABkEAEB,,AB,.:xA0,1PxB0.AB,AB()()rArB()()ABtrtr.,kkn,A,=()nrEA.AA.AAA,()rA.ii,11121212112212(,,,)(,,,)(,,,),,,nnnnnnPAAAA.AB,CD,ABCD.AB,()()fAfB,()()fAfB.12(,,,)TnfxxxXAXA12(,,,)TnXxxxABTBCAC.AB,,ABC.AB()()rArB12(,,,)TnfxxxXAXXCY2121(,,,)nniifxxxdy.,,()rA.id1-10,..A111100.12:AnC,1CACXCY,2121(,,,)nniifxxxdy,idA.12,,,nxxx12(,,,)0nfxxx...nA0A0AEQTQAQEPTAPP0A121TnCACCACi0.0iia0A.

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