推 icebergvodka:神光再臨~可否請神大再費心替小弟註解一下~QQ 10/02 01:13
→ icebergvodka:有些符號部分不太清楚了解~@@ 10/02 01:14
※ 引述《icebergvodka (肥嘟嘟左衛門)》之銘言：
: 請證明:
: 多變數的一階導數等於jacobian martix的determine
(x1,x2,...,xn), (y1,y2,...,yn)
dxi=(dxi/dyj)dyj=Jij dyj
dV=(1/n!)e(i1,i2,...,in)dxi1 dxi2 ... dxin
where e is full antisymmetric tensor and e(1,2,...,n)=1
dV=(1/n!)e(i1,i2,...,in) Ji1j1 Ji2j2... dyj1 dyj2...
=(1/n!)e(j1,j2,...,jn) det(J) dyj1 dyj2 ... dyjn
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