+ / -檢視主題
由 p 於 星期五 十一月 24, 2006 11:05 am
定義function δ of A#ed_op#BR#ed_cl#δ (A) = Σ(j=1~n)〔aij * (-1)i+j * Mij〕 ,(1≦ i ≦n)#ed_op#BR#ed_cl##ed_op#BR#ed_cl#你需要證明三件事#ed_op#BR#ed_cl#1.δ (A) is a n-linear function#ed_op#BR#ed_cl#2.δ (A)=0 when A has identical rows#ed_op#BR#ed_cl#3.δ (I)=1#ed_op#BR#ed_cl##ed_op#BR#ed_cl#證明了這三件事, 即得δ (A)=determinant (A).#ed_op#BR#ed_cl##ed_op#BR#ed_cl#(證明這三點, 就交給你自己處理) #ed_op#BR#ed_cl##ed_op#BR#ed_cl##ed_op#BR#ed_cl#n階行列式的定義:#ed_op#BR#ed_cl#determinant A of nxn is an alternating n-linear function #ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#
[數學]有誰會行列式餘因子展開的証明呢!?
由 相遇即是有緣 於 星期四 十一月 23, 2006 11:25 pm
#ed_op#P#ed_cl#設一個 n by n 矩陣 A#ed_op#/P#ed_cl##ed_op#P#ed_cl#則 |A| = Σ#ed_op#SUB#ed_cl#j=1#ed_op#/SUB#ed_cl##ed_op#SUP#ed_cl#n#ed_op#/SUP#ed_cl#〔a#ed_op#SUB#ed_cl#ij #ed_op#/SUB#ed_cl#* (-1)#ed_op#SUP#ed_cl#i+j #ed_op#/SUP#ed_cl#* M#ed_op#SUB#ed_cl#ij#ed_op#/SUB#ed_cl#〕#ed_op#SUB#ed_cl# ,#ed_op#/SUB#ed_cl#(1≦ i ≦n)#ed_op#/P#ed_cl##ed_op#P#ed_cl#以上為行列式 |A| 由某一列展開的結果,請問這個要怎麼證明呢!?#ed_op#/P#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#