[線代] 矩陣表示法的觀念

[mqazz1 (無法顯示)]

let L be the linear operator mapping R^3 into R^3 define by L(x) = Ax

    [ 3 -1 -2 ]             [1]              [1]             [ 0]
A = [ 2  0 -2 ]        v1 = [1]         v2 = [2]        v3 = [-2]
    [ 2 -1 -1 ]             [1]              [0]             [ 1]

find the transition matrix V corresponding to a change of basis from

{v1, v2, v3} to {e1, e2, e3}, and use it to determine the matrix B

representing L ith respect to {v1, v2, v3}

========================================================================

我是先令α={v1, v2, v3}, β={e1, e2, e3}

        [3 -1 -2]              β  [1 1  0]        α  [-2  1  2]
[L]   = [2  0 -2]       V = [I]  = [1 2 -2]     [I]  = [ 3 -1 -2]
   β   [2 -1 -1]              α  [1 0  1]        β  [ 2 -1 -1]


              α        [0  0  0]
B = [L]  = [I]   [L]  = [3 -1 -2]
       α     β    β  [2 -1 -1]

                    [0 0 0]
可是書上給的答案是B=[0 1 0]
                    [0 0 1]

請問我是甚麼地方錯了?

謝謝

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→ ert0700     :應該是矩陣表示的意義弄錯了   再看一下書
※ 編輯: mqazz1          來自: 61.228.26.1          (05/28 23:52)