Re: [理工] 線性代數
※ 引述《B90165 (abc)》之銘言：
: Prove that (AB)T = BT*AT, where A and B are matrices, and T represents the
: transpose operations
(AB)i,j = Σ[x=1~n](Ai,x * Bx,j) #definition of matrix multiplication
Ai,j=(AT)j,i ;; Bi,j=(BT)j,i #definition of transpose of matrix
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((AB)T)i,j = (AB)j,i = Σ[x=1~n]( Aj,x * Bx,i )
= Σ[x=1~n]( Bx,i * Aj,x )
= Σ[x=1~n]( (BT)i,x * (AT)x,j )
by definition of matrix multiplication => (AB)T =BT * AT #
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◆ From: 123.194.142.59
※ 編輯: cha122977 來自: 123.194.142.59 (03/15 04:06)
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