Re: [理工] 矩陣

[suhorng ( )]

※ 引述《Nolanly (V勝)》之銘言：
:                -1
: 題目:How will A   be affected if
: (a)the ith and jth rows of A are interchanged

http://en.wikipedia.org/wiki/Elementary_matrix#Row-switching_transformations

          -1    -1        -1    -1              -1
(T_{i,j}A)   = A   T_{i,j}   = A  T_{i,j} = 把 A   的第 i, j 個 column 交換

: (b)the ith row of A mutipilied by a nonzero scalar k

http://en.wikipedia.org/wiki/Elementary_matrix#Row-multiplying_transformations

         -1    -1      -1    -1               -1
(T_i(m)A)   = A  T_i(m)   = A  T_i(1/m) = 把 A   的第 i 個 column 乘以 1/m

: (c)k times the ith row of A is add to the row

http://en.wikipedia.org/wiki/Elementary_matrix#Row-addition_transformations

             -1    -1          -1    -1                  -1
(T_{j,i}(m)A)   = A  T_{j,i}(m)   = A  T_{j,i}(-m) = 把 A   的第 j 個
column 乘以 -m 加到第 i 個 column

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※ 編輯: suhorng         來自: 59.115.146.210       (04/06 17:03)
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