Exercise · ZW-SMOOTH-DIFFEOMORPHIC-DEFORMATION-010 · ★★☆ Intermediate
If \(\varphi\) and \(\psi\) are diffeomorphisms, what is the inverse of \(\psi\circ\varphi\)?
Choose one option.
Show answer
- D. \(\varphi^{-1}\circ\psi^{-1}\)
Explanation
The inverse of a composition reverses the order: \((\psi\circ\varphi)^{-1}=\varphi^{-1}\circ\psi^{-1}\).
Review the concept: Smooth diffeomorphic deformation
A smooth diffeomorphic deformation \(\varphi\) is a bijective, smooth transformation whose inverse is also smooth.
\[\varphi^{-1}\text{ is smooth}\]
More practice problems: smooth diffeomorphic deformation
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- ZW-SMOOTH-DIFFEOMORPHIC-DEFORMATION-007 What does it mean for the Jacobian of φ to be nonzero at every point?
- ZW-SMOOTH-DIFFEOMORPHIC-DEFORMATION-008 What is the velocity field in LDDMM?
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