[理學]2-4矩陣分塊法-全文預覽
【正文】 ??ssBABABA???????例 1 (P49) 設 ,1011012100100001????????????????A ,0211140110210101??????????????????B.AB求解 分塊成把 BA ,????????????????1011012100100001A???????????????10011001A00001121?,??????? EEO1A??????????????????0211140110210101B??????? 11B E21B 22B則 ?????????????2221111 BBEBEAOEAB.2212111111 ????????? BABBAEB.2212111111 ????????? BABBAEBAB又 21111 BBA ? ?????????????????????? ??110121011121??????????????? ??11012043 ,1142 ?????????????????????? ???02141121221 BA ,1333 ???????于是 ????????? 2212111111BABBAEBAB.1311334210410101??????????????????,100100000001???????????????bbaaA設?????????????bbaaB100000001000., ABABA ?求例 2 解 分塊將 BA ,???????????????bbaaA100100000001,0 021 ???????AA?????????????bbaaB100000001000,0 021 ???????BB其中 ,0 11 ???????aaA。32 1112 ??????????A?????????????12111AOOAA。 若把 A按行塊，則方程組可寫為： 1122TTTmmbbxb????? ???? ???? ????? ???? ????????若把 A按列分塊，則方程組可寫為： ? ?12121 1 2 2nnnnxxa a a bxx a x a x a b?????? ???????? ? ? ?即 例 4（ P51） 證明矩陣 A＝ 0的充分必要條件是方陣 ATA＝ 0 證：必要性顯然?！≈?jù)逆陣的唯一性有 ， 及由bAx，bAxb ，Ax11 ,0A??????（ 3） ),1 , 21)(111,11122112211222221112121112121222211211121*1**1njDDAbAbAbDxAbAbAbAbAbAb
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