- #1
mnb96
- 715
- 5
Hello,
let's suppose I have two functions [itex]\phi:U\rightarrow V[/itex], and [itex]T:V\rightarrow V[/itex] that are both diffeomorphisms having inverse.
Furthermore [itex]T[/itex] is linear.
I consider the function [itex]f(u) = (\phi^{-1}\circ T \circ \phi)(u)[/itex], where [itex]\circ[/itex] is the composition of functions.
Since [itex]T[/itex] is linear, we already know that the Jacobian determinant is constant: [itex]J_T(v)=\lambda[/itex].
What can we say about [itex]J_f(u)[/itex], the Jacobian of f ?
let's suppose I have two functions [itex]\phi:U\rightarrow V[/itex], and [itex]T:V\rightarrow V[/itex] that are both diffeomorphisms having inverse.
Furthermore [itex]T[/itex] is linear.
I consider the function [itex]f(u) = (\phi^{-1}\circ T \circ \phi)(u)[/itex], where [itex]\circ[/itex] is the composition of functions.
Since [itex]T[/itex] is linear, we already know that the Jacobian determinant is constant: [itex]J_T(v)=\lambda[/itex].
What can we say about [itex]J_f(u)[/itex], the Jacobian of f ?