Hello,

The relation between J and J* is that : J×J* = 1. You can clearly see this thing by their formulas.

Suppose we have a function given,

F(x) = { u(x,y) , v(x,y) }

Now its jacobian is given by , J =  d(u,v)/d(x,y)

And it is equal to,

= [ du/dx   du/dy

dv/dx    dv/dy ]

Hope it helps.