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19123452.11mnnm×ija⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛mnmmnnaaaaaaaaaLLLLLLL212222111211,nm×ijijanmA×}{ijaA=nmijaA×=}{.⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−1131032132121nmnxxx,,,21L⎪⎪⎩⎪⎪⎨⎧=+++=+++=+++mnmnmmnnnnbxaxaxabxaxaxabxaxaxaLLLLLL2211222221211121211120ijaib)1(+×nm⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛mmnmmnnbaaabaaabaaaLLLLLLLL21222221111211⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−113103213212A.nm=nnAnnaaa,,,2211LL1==nm()11aA=.11anmijaA×=}{nmijbB×=}{,,,1;,,1,njmibaijijLL===O.nmO×}{ijaA=n1Ajiaij∀=,0A2Ajiaij∀=,0A⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nnnnaaaaaaALLLLLLL00022211211⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nnnnaaaaaaALLLLLLL21222111000jiaij≠∀=,021⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nnaaaALLLLLLL0000002211}{},,{,2211iinnadiagaaadiagA==L.KK=)(kdiag1InnI⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=100010001LMOMMLLI012.22}{ijaA=}{ijbB=nm×ABA+Bnm×BAcCij+==}{⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛+++++++++=mnmnmmmmnnnnbababababababababaLLLLLLL221122222221211112121111.2,,⎟⎟⎠⎞⎜⎜⎝⎛−=2015A⎟⎟⎠⎞⎜⎜⎝⎛−=4012B⎟⎟⎠⎞⎜⎜⎝⎛=dbcaCBA+.BAC+=dcba,,,22nmijaA×=}{}{ijaA−=−A:)(BABA−+=−⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−−−−−−−−−=mnmnmmmmnnnnbababababababababaLLLLLLL221122222221211112121111OCBA,,,1ABBA+=+2)()(CBACBA++=++3AOA=+4OAA=−3λnmijaA×=}{AλλAnm×λλAAcCij===}{⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=mnmmnnaaaaaaaaaλλλλλλλλλLLLLLLL212222111211OBA,,µλ,1BABAλλλ+=+)(2AAAµλµλ+=+)(3)()(AAµλλµ=4OA=⋅0233⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−=345751213A⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−=123915457B,2BXA=+X.4}{ijaA=sm×}{ijbB=ABABns×nm×}{ijcABC==∑==+++=skkjiksjisjijiijbabababac12211L),,2,1;,,2,1(njmiLL==.1ABAB2C=ABAB3C=ABAB),(jiij4.⎟⎟⎠⎞⎜⎜⎝⎛−=20121301A⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−=431102311014BABBA.5AIAAI=IA=A⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛21422142100110012142246An×1B1×n()naaaAL21=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nbbbBM21ABBA.()102−=A⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=011B2=AB.⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−=000102102BA7,⎟⎟⎠⎞⎜⎜⎝⎛−−=⎟⎟⎠⎞⎜⎜⎝⎛=1122,2142BAABBA.;.⎟⎟⎠⎞⎜⎜⎝⎛=0000AB⎟⎟⎠⎞⎜⎜⎝⎛−−=2142BAABBA4ABBA67ABBA()ABBAAB=AB1IAAI=237OAB=OA≠OB≠ACAB=OA≠CB=251ACABCBA+=+)(CABAACB+=+)(2)()(BCACAB=3)()()(BABAABλλλ==,λ4AIAAI==(I)(II)),(ji2}{ijaA=sm×}{ijbB=ts×}{ijcC=nt×ABdDij==}{tm×∑==sllkilikbad1BCeEij==}{ns×∑==tkkjlkljcbe1)(BCA)(BCAnm×DCCABP==)(AEBCAQ==)(ijijqp=8ABABABABABC=∑==skkjikijbac1jicij=,0iiiiiibac=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−=300020121A⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−=200020133BAn)(,,,121kkAAAAAAAA===+L,kIA=0.lklkAAA=+kllkAA=)(kkkBAAB≠)(26222222)(BABABBAABABA++≠+++=+9,,0000100001000010⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=A,000100010001⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=λλλλBAn4A)4(≥nBnK∑=+=−niiniinnAKCAK0)(5()⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=mnmmnnaaaaaaaaaALLLLLLL212222111211⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=mnnnmmTaaaaaaaaaALLLLLLL212221212111AAmn×TAAjiijTAA)()(=TA),(ji),(ij10,⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−=4312,232014BATAB)(TTABTTBATTTABAB=)(TTTBAAB=)(1AATT=)(2TTTBABA+=+)(3λλλ,)()(TTAA=274.)(TTTABAB=6()}{ijaA=nAAjiaaTjiij=⇔∀=,AAjiaaTjiij−=⇔∀−=,Aiaii∀=0⎟⎟⎠⎞⎜⎜⎝⎛−=0111A⎟⎟⎠⎞⎜⎜⎝⎛−=0110B1ABBA±AB⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛−=0110,0111BA⎟⎟⎠⎞⎜⎜⎝⎛−=1011AB2ABABBABAAB=3AAATλ,4A)(21TAAH+≡)(21TAAS−≡SHA+=11A02=A0=A7()A}{ijaA=n∑==niiiaAtr1)(28nnnnnnaaaaaaaaaLLLLLLL212222111211A|A|det()A1).()(BAtrABtr=21||||AAT=33||||AAnλλ=⎟⎟⎠⎞⎜⎜⎝⎛−=1312A⎟⎟⎠⎞⎜⎜⎝⎛−=3936BAB3=45||,5||==BA||B=4559||3|3|2=×==AA||||AAλλ=4||||||BAAB=3632×BIOAbbbbbbbbbaaaaaaaaaD−=−−−=333231232221131211333231232221131211100010001000000000.1.11,=D||||BAD131211,,bbb333231232221133112311131333231132112211121232221131112111111131211100010000001bbbbbbbababaaaabababaaaabababaaaaD−−−=232221,,bbb333231,,bbb29OIABAbababaaaabababaaaabababaaaaDkkkkkkkkkkkkkkkkkkkkkkkkkkk−=−−−=∑∑∑∑∑∑∑∑∑=========0001000000100000013133312331133332313132312231122322213131312131111312113,2,1,3=⇔+jrrjjABAOID−−=3)1(1.11|,|||)1()1(||||)1(333ABABABID=−−=−−=8()|A|}{ijaA=ijA⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nnnnnnAAAAAAAAAALLLLLLL212221212111*A*A),(jiA),(ij⎟⎟⎠⎞⎜⎜⎝⎛=4321A⎟⎟⎠⎞⎜⎜⎝⎛−−=1324*A1IAAAAA||**==*AAB=1.31.3⎩⎨⎧≠==+++=ijijAAaAaAabjninjijiij,0,||2211L⇒IAAA||*=3012⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=343122321A⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−−−=222563462*A=AA*IAE||2200020002==⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛2||=AIAAA||*=13nA*)(Ak*1*)(AkAkn−=2.39AnBIBAAB==BAAA⎟⎟⎠⎞⎜⎜⎝⎛=1302A⎟⎟⎠⎞⎜⎜⎝⎛=−102321BA11−AABCACICCBAACBBIB=====)()(2A0||≠A0||≠A*1||1AAA=−IAA=−11||||||||11===−−IAAAA0||≠A.311IAAAAA||**==0||≠AIAAAAAA==)||1()||1(**0||=A14⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=343122321A112AA*1||1AAA=−=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−−−22256346221IAB=IBA=A1−=AB1||||||||===IABBA0||≠A1−A1111)()(−−−−=====AIAABABAABIBIAA22=−IAA2,+11)2(,−−+IAAIIAIAIIAA3)2)(3(,2)(−=+−=−⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nnnnnnaaaaaaaaaALLLLLLL212222111211⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nxxxXM21⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛=nbbbBM21BAX=,A0||≠A1−ABAX1−=.16⎪⎩⎪⎨⎧=++=++−=++0343122232321321321xxxxxxxxx32BAX1−==⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−−−−101012222563462212.A1−AAA=−−11)(3A0≠λAλ111)(−−=AAλλ.4AB.AB111)(−−−=ABAB5.ATATTAA)()(11−−=6A||1||1AA=−.1||||||||11===−−IAAAA7A1−A0||≠AkkAA)(1−−=17A2.433⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−−−=⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−=0211140110212301,1011012100100001BAABABAB422×⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛=22211211212,BBBBBIAOIABA,⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=22211211212BBBBIAOIAB=⎟⎟⎠⎞⎜⎜⎝⎛++22121211111211BBABBABB21111BBA+22121BBA+⎟⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎜⎝⎛−−−=3511114210212301AB.=+BA⎟⎟⎠⎞⎜⎜⎝⎛+++22221112112BIBABBI⎟⎟⎠⎞⎜⎜⎝⎛=2123333IAOIAAB4⎟⎟⎠⎞⎜⎜⎝⎛=22211211AAAAA⎟⎟⎠⎞⎜⎜⎝⎛=22211211BBBBB⎟⎟⎠⎞⎜⎜⎝⎛=01000111A⎟⎟⎠⎞⎜⎜⎝⎛=0012A⎟⎟⎠⎞⎜⎜⎝⎛−=01112121A⎟⎟⎠⎞⎜⎜⎝⎛=1022A⎟⎟⎠⎞⎜⎜⎝⎛−=02130111B⎟⎟⎠⎞⎜⎜⎝⎛=1212B⎟⎟⎠⎞⎜⎜⎝⎛−−=21140121B⎟⎟⎠⎞⎜⎜⎝⎛=0122B⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=2221121122211211BBBBAAAAAB=⎟⎟⎠⎞⎜⎜⎝⎛++++222212121212211212212121121121111BABABABABABABABA34AB⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−=40102130111B⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛=11212B()21121−−=B()022=BAB⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=2221121122211211BB