[理工] [線代]-基底變換

[mdpming (阿阿 要加油)]

1.


α = { (1,-1) , (-2,3) }

β = { (1,1)  . (0,1) }


                  2
be two bases for R and let A = [2 1]
                               [0 3]


                      2         2
be the matrix for T: R ------> R relative to α


<1> find transtion matrix p from β to α
                                                         T
<2> Using p and A find V   and [T(V)]   where V  = (1,-3)
                        α           α        β



sol:

<1>

設題意之 p 為 change of coordinate matrix from β to α

另


 U = [ 1 -2]  ,  V = [1 0]
     [-1  3]         [1 1]


X = UX  = VX
      α    β


....
....


<2>

另 TX = Y


X = UX   , Y = UY
      α         α

.....
.....


這是筆記理的解答


像<2>小題我該如何判斷 X = UX   , Y = UY
                            α         α


因為有些題目 Y = VY
                   β

要怎麼看 困擾我好久了...



2.

詹森 控制 p12-39 那一題 他給

        1
G(S) = ---  有什麼用處 感覺沒有用到也..
         2
        s



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