推 goodguychung:謝謝:) 02/28 21:48
※ 引述《goodguychung (泡麵終結者)》之銘言：
: give any p(x)=a+bx+cx^2 in P3,to find the coordinates of p(x) with
: respect to[1,2x,4x^2-2]
: 請問這題該如何計算呢?
取β={1,x,x^2} γ={1,2x,4x^2-2}
γ
欲求 [p(x)]
β
1 0 0
[p(x)] = [0 1 0]
β 0 0 1
1
[ 0 ] = x (1) + y (2x) + z (4x^-2) => x=1 y=0 z=0
0
0
[ 1 ] = x (1) + y (2x) + z (4x^-2) => x=0 y=1/2 z=0
0
0
[ 0 ] = x (1) + y (2x) + z (4x^-2) => x=1/2 y=0 z=1/4
1
γ 1 0 1/2
所以答案是 [p(x)] = [ 0 1/2 0 ]
β 0 0 1/4
不知道對不對
請神人來更正吧!
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