If one does the substitution as mentioned here, the left side will be Jacobian of an identity map isn’t it? How to compute that and how to conclude that the Jacobian here is invertible.
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danny
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In the identity, $u(x,y)=x$ and $v(x,y)=y$ etc. – Angina Seng Dec 18 '19 at 16:17
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In the left hand side we have Jacobian of phi and it’s inverse. What happens in this case? – danny Dec 18 '19 at 16:22
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Look at the formula for $J(\Psi)$: substitute in $u(x,y)=x$ and $v(x,y)=y$. – Angina Seng Dec 18 '19 at 16:24
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2The Jacobian of any linear map is just the matrix that represents that map. – amd Dec 18 '19 at 20:32