分块矩阵的初等变换

《分块矩阵的初等变换》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、©¬ÝÐC†•ïJJian-BiaoChenMathematicandComputerSciencesSMU†,ü1¬½n1.©¬ÝAŠ˜g¬GÐ1C†¤ÝAbuA†¦˜‡ƒA¬GÐbI.e¡©Oén«¬GÐ1C†?1•[?Ø"5¿µéuÐ1C†,I•ꇆA1êƒÓü§…I1©¬•ªÑ‡†A1©¬•ªƒÓ"bI(ri;rj)A=Ab(ri;rj)Ù¥Ab(ri;rj)9bI(ri;rj)©O•†A1i;j1¬9I1i;j1¬¤§=XJ2323A11A12





A1tA11A12

2、





A1t6......76......76...76...766Ai1Ai2





Ait7766Aj1Aj2





Ajt776...7ri$rj6...7A=6......7!6......7=Ab(ri;rj)66Aj1Aj2





Ajt7766Ai1Ai2





Ait774...54...5............As1As2





AstAs1As2





AstÙ¥§Aij•minjÝ"Jian-BiaoChenMathematicandComputerSciences

3、SMU†,ü1¬2323ImIm116..76..76.76.76Im760Im76i76j76.7ri$rj6.7I=66..77!66..77=bI(ri;rj)66Imj7766Imi0774...54...5ImsImsÙ¥§Imk•mküÝ"KkbI(ri;rj)A=Ab(ri;rj)Jian-BiaoChenMathematicandComputerSciencesSMU,1¬†¦M5¿µéuÐ1C†,I•ꇆA1êƒÓü§…I1©¬•ªÑ‡†A1©¬•ªƒÓ"bIMrA=AbMriiÙ¥

4、AbMri9bIMri©O•A1i1¬9I1i1¬†¦M¤§=XJ2A11A12





A1t32A11A12





A1t3......6...76...76...7Mri6...7A=6Ai1Ai2





Ait7!6MAi1MAi2





MAit7=AbMr4545i..................As1As2





AstAs1As2





AstÙ¥§Aij•minjÝ"Jian-BiaoChenMathematicandComputerSciencesSMU,1¬†¦M23

5、23ImIm1166...7766...7767Mri67I=6Imi7!6MImi7=bIMri4..54..5..ImsImsÙ¥§Imk•mküÝ"KkbIMrA=AbMriid?ÝMê†A1i1¬ÝAik(k=1;2;:::;t)1êƒÓ,=§M•U(MAik$ŽŒ1?¿Ý"Jian-BiaoChenMathematicandComputerSciencesSMU,1¬†¦ÝM,˜1¬(5¿µéuÐ1C†§I•ꇆA1êƒÓü§…I1©¬•ªÑ‡†A1©¬•ªƒÓ")bIMrA=

6、AbMri+rji+rjÙ¥AbMri+rj9bIMri+rj©O•A1i1¬†¦MA1j1¬§9I1i1¬†¦MI1j1¬¤§=XJ2323A11A12





A1tA11A12





A1t6......76......76...76...766Ai1Ai2





Ait7766Ai1Ai2





Ait776...7Mri+rj6...7A=6......7!6......7=AbMri+rj66Aj1Aj2





Ajt7766MAi1+Aj1MAi2+Aj2





MAi

7、t+Ajt774...54...5............As1As2





AstAs1As2





AstÙ¥§Aij•minjÝ"Jian-BiaoChenMathematicandComputerSciencesSMU,1¬†¦ÝM,˜1¬2323ImIm1166...7766...776Im76Im76i76i76..7Mri+rj6.7I=66.77!66..77=bIMri+rj6Im76MIm76j76j74..54..5..ImsImsÙ¥§Imk•mküÝ"KkbIMrA=AbMri

8、+rji+rjd?ÝMê†A1i1¬ÝAik(k=1;2;:::;t)1êƒÓ,¿…ÝM1ê†A1j1¬ÝAjk(k=1;2;:::;t)1êƒÓ"=,M•U(MAik+Ajk$ŽŒ1?¿Ý"Jian-BiaoChenMathematica