A
Consider linear equations
u=ax+by
v = cx + dy
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If we take (0,0) in the xy plane, (1,0), (0,1), (1,1) 4 dots becomes a square with a 1, then through
[a b
c d] conversion will be made after a parallelogram. In the uv plane is <a, b>, <c, d> two vectors
Area Vector | <a, b> x <c, d> | = ad-cd this transform is represented by the area of the ad-cb / 1 ratio of the area of original
Equal to the corresponding equations have determinant
B
x = g (u, v) y = h (u, v), x, y and uv not linear
But after doing a full differential, dx = Gu du + Gv dv, dy = Hu du + Hv dv
Dxdy visible infinitesimal dudv in the specified point (u0, v0) is a linear relationship. dxdy, dudv area ratio
| to gv
Hu Hv | That Jacobian (not the determinant 0) that is dxdy / dudv = J so do the integral transformation when dxdy = J * dudv